{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fast Fourier Transform Forecasting Model (FFT)\n",
    "The following is a brief demonstration of the FFT forecasting model. This model is especially suited for data that is very seasonal. The datasets chosen for this demonstration were selected accordingly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fix python path if working locally\n",
    "from utils import fix_pythonpath_if_working_locally\n",
    "fix_pythonpath_if_working_locally()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "from darts import TimeSeries\n",
    "from darts.models import (\n",
    "    FFT,\n",
    "    AutoARIMA,\n",
    "    ExponentialSmoothing,\n",
    "    Prophet,\n",
    "    Theta\n",
    ")\n",
    "from darts.metrics import mape\n",
    "from darts.utils.missing_values import fill_missing_values\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "import logging\n",
    "logging.disable(logging.CRITICAL)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Read and format\n",
    "Here we simply read the CSV file containing daily temperatures, and transform the values into the desired format."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('temps.csv')\n",
    "df['temps'] = df['Daily minimum temperatures'].str.replace('^[^\\d]*', '').astype(float)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constructing `TimeSeries` instances for training and validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "output_type": "error",
     "ename": "KeyError",
     "evalue": "\"None of [Index(['temps'], dtype='object')] are in the [columns]\"",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-15-d884f4ab8cad>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mts\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfill_missing_values\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mTimeSeries\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfrom_dataframe\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'Date'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m'temps'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'auto'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mtrain\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mval\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mts\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msplit_after\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mTimestamp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'19850701'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mtrain\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mval\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/Desktop/Darts/darts/darts/timeseries.py\u001b[0m in \u001b[0;36mfrom_dataframe\u001b[0;34m(df, time_col, value_cols, freq, fill_missing_dates)\u001b[0m\n\u001b[1;32m    557\u001b[0m                 \u001b[0mvalue_cols\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mvalue_cols\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    558\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 559\u001b[0;31m             \u001b[0mseries_df\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdf\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mvalue_cols\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    560\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    561\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mtime_col\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/anaconda3/envs/darts-dev/lib/python3.8/site-packages/pandas/core/frame.py\u001b[0m in \u001b[0;36m__getitem__\u001b[0;34m(self, key)\u001b[0m\n\u001b[1;32m   2903\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mis_iterator\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2904\u001b[0m                 \u001b[0mkey\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2905\u001b[0;31m             \u001b[0mindexer\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mloc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_get_listlike_indexer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mraise_missing\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2906\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2907\u001b[0m         \u001b[0;31m# take() does not accept boolean indexers\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/anaconda3/envs/darts-dev/lib/python3.8/site-packages/pandas/core/indexing.py\u001b[0m in \u001b[0;36m_get_listlike_indexer\u001b[0;34m(self, key, axis, raise_missing)\u001b[0m\n\u001b[1;32m   1252\u001b[0m             \u001b[0mkeyarr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mindexer\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnew_indexer\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0max\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_reindex_non_unique\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkeyarr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1253\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1254\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_validate_read_indexer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkeyarr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mindexer\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mraise_missing\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mraise_missing\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1255\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mkeyarr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mindexer\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1256\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/anaconda3/envs/darts-dev/lib/python3.8/site-packages/pandas/core/indexing.py\u001b[0m in \u001b[0;36m_validate_read_indexer\u001b[0;34m(self, key, indexer, axis, raise_missing)\u001b[0m\n\u001b[1;32m   1296\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mmissing\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mindexer\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1297\u001b[0m                 \u001b[0maxis_name\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mobj\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_get_axis_name\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maxis\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1298\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0mKeyError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf\"None of [{key}] are in the [{axis_name}]\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1299\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1300\u001b[0m             \u001b[0;31m# We (temporarily) allow for some missing keys with .loc, except in\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyError\u001b[0m: \"None of [Index(['temps'], dtype='object')] are in the [columns]\""
     ]
    }
   ],
   "source": [
    "ts = fill_missing_values(TimeSeries.from_dataframe(df, 'Date', ['temps']), 'auto')\n",
    "train, val = ts.split_after(pd.Timestamp('19850701'))\n",
    "train.plot()\n",
    "val.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic FFT model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = FFT(required_matches=set(), nr_freqs_to_keep=None)\n",
    "model.fit(train)\n",
    "pred_val = model.predict(len(val))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot below shows us that a simple DFT with a random train-test split will most likely lead to bad results. Upon closer inspection we can see that the prediction (in green) simply repeats the training set (blue). This is the standard behavior of the DFT, and by itself it is quite useless, since repeating our training set could be done much more efficiently. Three improvements were made to this approach."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "MAPE: 416130884490747.6\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
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125.315092 \nL 89.357361 117.047411 \nL 89.540763 135.085987 \nL 89.724165 117.047411 \nL 89.815866 123.06027 \nL 89.907567 120.05384 \nL 89.999268 74.205793 \nL 90.090969 100.51205 \nL 90.182669 99.760442 \nL 90.27437 110.282945 \nL 90.366071 96.002406 \nL 90.549473 117.047411 \nL 90.641174 111.78616 \nL 90.824576 133.582772 \nL 90.916277 97.50562 \nL 91.007978 99.760442 \nL 91.191379 117.047411 \nL 91.374781 92.244369 \nL 91.466482 96.002406 \nL 91.558183 81.721867 \nL 91.649884 92.244369 \nL 91.741585 76.460615 \nL 91.924987 132.831165 \nL 92.016688 129.073128 \nL 92.108388 103.518479 \nL 92.200089 123.811877 \nL 92.29179 118.550626 \nL 92.383491 92.995976 \nL 92.475192 98.257228 \nL 92.750295 146.360097 \nL 93.025397 119.302233 \nL 93.117098 119.302233 \nL 93.208799 128.321521 \nL 93.3005 111.034552 \nL 93.392201 114.792589 \nL 93.483902 127.569914 \nL 93.575603 99.008835 \nL 93.667304 121.557055 \nL 93.759005 87.734725 \nL 93.942407 135.085987 \nL 94.034107 97.50562 \nL 94.125808 134.33438 \nL 94.400911 107.276516 \nL 94.492612 109.531338 \nL 94.584313 78.715437 \nL 94.676014 84.728296 \nL 94.767715 117.047411 \nL 94.859416 94.499191 \nL 94.951116 102.766872 \nL 95.042817 92.995976 \nL 95.226219 45.644715 \nL 95.409621 95.250798 \nL 95.501322 88.486333 \nL 95.684724 118.550626 \nL 95.776425 109.531338 \nL 95.959826 53.160788 \nL 96.143228 112.537767 \nL 96.234929 105.773301 \nL 96.32663 108.028123 \nL 96.418331 96.754013 \nL 96.510032 66.68972 \nL 96.693434 106.524908 \nL 96.968536 61.428469 \nL 97.151938 65.186505 \nL 97.243639 49.402751 \nL 97.33534 60.676861 \nL 97.427041 48.651144 \nL 97.518742 59.925254 \nL 97.610443 102.015264 \nL 97.793844 53.160788 \nL 97.977246 108.77973 \nL 98.068947 105.773301 \nL 98.160648 56.167217 \nL 98.34405 100.51205 \nL 98.435751 116.295804 \nL 98.527452 115.544196 \nL 98.619153 120.805448 \nL 98.802554 82.473474 \nL 98.894255 98.257228 \nL 98.985956 89.23794 \nL 99.077657 92.244369 \nL 99.261059 119.302233 \nL 99.35276 139.595631 \nL 99.536162 120.05384 \nL 99.719563 139.595631 \nL 99.811264 110.282945 \nL 99.902965 114.040982 \nL 99.994666 120.805448 \nL 100.086367 118.550626 \nL 100.178068 156.130992 \nL 100.269769 131.32795 \nL 100.36147 134.33438 \nL 100.544872 164.398673 \nL 100.636572 171.914746 \nL 100.911675 98.257228 \nL 101.003376 131.32795 \nL 101.095077 126.818306 \nL 101.186778 128.321521 \nL 101.37018 168.156709 \nL 101.461881 164.398673 \nL 101.645282 148.614919 \nL 101.736983 154.627777 \nL 102.012086 90.741155 \nL 102.195488 135.837594 \nL 102.37889 117.047411 \nL 102.470591 149.366526 \nL 102.837394 113.289374 \nL 102.929095 111.78616 \nL 103.020796 113.289374 \nL 103.112497 134.33438 \nL 103.204198 117.047411 \nL 103.295899 127.569914 \nL 103.3876 117.047411 \nL 103.479301 130.576343 \nL 103.571001 113.289374 \nL 103.662702 117.799018 \nL 103.754403 163.647065 \nL 103.937805 105.773301 \nL 104.212908 180.182427 \nL 104.304609 177.927605 \nL 104.48801 152.372955 \nL 104.671412 168.156709 \nL 104.763113 156.130992 \nL 104.854814 115.544196 \nL 104.946515 125.315092 \nL 105.038216 165.901887 \nL 105.221618 123.811877 \nL 105.405019 158.385814 \nL 105.588421 132.079558 \nL 105.680122 133.582772 \nL 105.771823 174.921175 \nL 105.863524 157.634207 \nL 105.955225 172.666353 \nL 106.138627 142.60206 \nL 106.230328 162.143851 \nL 106.322029 152.372955 \nL 106.413729 156.130992 \nL 106.50543 179.430819 \nL 106.688832 160.640636 \nL 106.872234 143.353667 \nL 107.055636 192.208144 \nL 107.147337 203.482254 \nL 107.239038 195.96618 \nL 107.422439 127.569914 \nL 107.605841 165.15028 \nL 107.697542 154.627777 \nL 107.789243 155.379385 \nL 107.880944 189.953322 \nL 107.972645 185.443678 \nL 108.064346 169.659924 \nL 108.156047 184.692071 \nL 108.431149 141.098845 \nL 108.52285 143.353667 \nL 108.614551 160.640636 \nL 108.706252 153.87617 \nL 108.797953 154.627777 \nL 108.981355 148.614919 \nL 109.073056 152.372955 \nL 109.164757 196.717788 \nL 109.348158 170.411531 \nL 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120.05384 \nL 120.077164 158.385814 \nL 120.260566 103.518479 \nL 120.443968 156.882599 \nL 120.62737 133.582772 \nL 120.71907 133.582772 \nL 120.902472 115.544196 \nL 121.085874 171.914746 \nL 121.177575 141.098845 \nL 121.269276 159.889029 \nL 121.360977 133.582772 \nL 121.452678 139.595631 \nL 121.544379 92.995976 \nL 121.636079 102.015264 \nL 121.72778 105.773301 \nL 121.819481 95.250798 \nL 122.002883 108.028123 \nL 122.277986 82.473474 \nL 122.461388 129.073128 \nL 122.644789 115.544196 \nL 122.73649 124.563484 \nL 122.828191 99.760442 \nL 123.011593 123.811877 \nL 123.103294 111.034552 \nL 123.194995 132.831165 \nL 123.286696 124.563484 \nL 123.378397 90.741155 \nL 123.470098 102.015264 \nL 123.561798 130.576343 \nL 123.7452 102.015264 \nL 123.836901 103.518479 \nL 123.928602 102.015264 \nL 124.020303 114.792589 \nL 124.112004 61.428469 \nL 124.203705 79.467045 \nL 124.295406 123.06027 \nL 124.387107 89.23794 \nL 124.478807 111.034552 \nL 124.570508 83.225081 \nL 124.845611 131.32795 \nL 125.029013 61.428469 \nL 125.120714 79.467045 \nL 125.212415 68.192935 \nL 125.579218 132.079558 \nL 125.670919 92.244369 \nL 125.76262 93.747584 \nL 125.854321 117.047411 \nL 125.946022 114.040982 \nL 126.037723 100.51205 \nL 126.129424 120.805448 \nL 126.404526 74.957401 \nL 126.496227 79.467045 \nL 126.587928 77.96383 \nL 126.679629 129.073128 \nL 126.77133 125.315092 \nL 126.863031 123.06027 \nL 126.954732 103.518479 \nL 127.229835 135.837594 \nL 127.413236 73.454186 \nL 127.596638 130.576343 \nL 127.688339 135.085987 \nL 127.78004 104.270086 \nL 127.963442 123.811877 \nL 128.055143 104.270086 \nL 128.146844 131.32795 \nL 128.330245 97.50562 \nL 128.421946 108.028123 \nL 128.605348 79.467045 \nL 128.697049 102.015264 \nL 128.78875 95.250798 \nL 128.880451 98.257228 \nL 128.972152 96.002406 \nL 129.063853 89.989547 \nL 129.155554 112.537767 \nL 129.247254 111.034552 \nL 129.522357 89.989547 \nL 129.614058 107.276516 \nL 129.79746 72.702579 \nL 129.889161 74.205793 \nL 129.980862 105.773301 \nL 130.072563 90.741155 \nL 130.347665 126.818306 \nL 130.439366 101.263657 \nL 130.531067 130.576343 \nL 130.622768 113.289374 \nL 130.714469 120.05384 \nL 130.80617 148.614919 \nL 131.081273 105.773301 \nL 131.172973 68.192935 \nL 131.356375 111.034552 \nL 131.448076 135.837594 \nL 131.539777 111.034552 \nL 131.631478 129.073128 \nL 131.723179 97.50562 \nL 131.81488 131.32795 \nL 131.998282 108.028123 \nL 132.089983 132.831165 \nL 132.181683 108.028123 \nL 132.273384 111.034552 \nL 132.365085 101.263657 \nL 132.548487 123.811877 \nL 132.82359 80.970259 \nL 132.915291 144.105275 \nL 133.006992 138.092416 \nL 133.098692 159.137421 \nL 133.190393 149.366526 \nL 133.373795 99.760442 \nL 133.557197 141.850453 \nL 133.648898 137.340809 \nL 133.8323 153.124563 \nL 134.107402 120.805448 \nL 134.199103 147.111704 \nL 134.290804 141.850453 \nL 134.382505 138.844024 \nL 134.565907 124.563484 \nL 134.749309 133.582772 \nL 134.84101 118.550626 \nL 134.932711 141.098845 \nL 135.024411 111.78616 \nL 135.116112 132.079558 \nL 135.207813 115.544196 \nL 135.299514 117.047411 \nL 135.391215 138.092416 \nL 135.482916 115.544196 \nL 135.574617 144.856882 \nL 135.666318 131.32795 \nL 135.84972 149.366526 \nL 136.033121 120.805448 \nL 136.124822 165.901887 \nL 136.399925 104.270086 \nL 136.675028 189.953322 \nL 136.766729 188.450107 \nL 136.85843 171.914746 \nL 136.95013 173.417961 \nL 137.225233 140.347238 \nL 137.316934 177.927605 \nL 137.408635 167.405102 \nL 137.500336 178.679212 \nL 137.867139 144.105275 \nL 137.95884 149.366526 \nL 138.050541 143.353667 \nL 138.142242 123.811877 \nL 138.325644 144.856882 \nL 138.509046 154.627777 \nL 138.600747 141.098845 \nL 138.692448 168.156709 \nL 138.784149 159.889029 \nL 138.875849 132.831165 \nL 139.059251 149.366526 \nL 139.150952 147.111704 \nL 139.334354 121.557055 \nL 139.517756 160.640636 \nL 139.609457 131.32795 \nL 139.701158 144.856882 \nL 139.792858 138.844024 \nL 139.884559 185.443678 \nL 139.97626 177.175997 \nL 140.067961 153.124563 \nL 140.159662 193.711358 \nL 140.251363 182.437249 \nL 140.434765 131.32795 \nL 140.526466 179.430819 \nL 140.618167 174.921175 \nL 140.709867 139.595631 \nL 140.893269 198.221002 \nL 141.076671 152.372955 \nL 141.168372 150.118133 \nL 141.260073 138.844024 \nL 141.443475 160.640636 \nL 141.810278 144.105275 \nL 141.901979 156.130992 \nL 142.085381 196.717788 \nL 142.177082 185.443678 \nL 142.268783 204.985468 \nL 142.360484 198.97261 \nL 142.452185 159.137421 \nL 142.543886 160.640636 \nL 142.727287 147.863311 \nL 142.818988 148.614919 \nL 142.910689 154.627777 \nL 143.094091 214.004756 \nL 143.185792 207.991898 \nL 143.277493 156.130992 \nL 143.369194 160.640636 \nL 143.460895 154.627777 \nL 143.552596 180.182427 \nL 143.644296 175.672783 \nL 143.827698 163.647065 \nL 143.919399 153.87617 \nL 144.0111 158.385814 \nL 144.194502 180.182427 \nL 144.377904 141.850453 \nL 144.469605 162.143851 \nL 144.653006 135.085987 \nL 144.744707 128.321521 \nL 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114.040982 \nL 231.402061 120.805448 \nL 231.585463 82.473474 \nL 231.768865 140.347238 \nL 231.860566 138.092416 \nL 231.952267 129.824736 \nL 232.043968 143.353667 \nL 232.135669 126.066699 \nL 232.22737 128.321521 \nL 232.31907 135.837594 \nL 232.410771 133.582772 \nL 232.502472 117.047411 \nL 232.685874 74.205793 \nL 232.960977 129.824736 \nL 233.144379 114.792589 \nL 233.32778 137.340809 \nL 233.419481 117.047411 \nL 233.511182 122.308662 \nL 233.602883 97.50562 \nL 233.694584 138.092416 \nL 233.786285 133.582772 \nL 233.969687 114.792589 \nL 234.061388 126.818306 \nL 234.33649 102.766872 \nL 234.428191 62.931683 \nL 234.794995 159.889029 \nL 234.978397 81.721867 \nL 235.070098 92.244369 \nL 235.253499 141.850453 \nL 235.3452 156.130992 \nL 235.620303 108.77973 \nL 235.712004 161.392243 \nL 235.803705 153.87617 \nL 235.895406 156.130992 \nL 235.987107 135.085987 \nL 236.170508 147.111704 \nL 236.35391 86.231511 \nL 236.445611 88.486333 \nL 236.720714 162.143851 \nL 236.904116 140.347238 \nL 237.087517 129.824736 \nL 237.179218 126.066699 \nL 237.36262 161.392243 \nL 237.546022 141.098845 \nL 237.637723 135.085987 \nL 237.821125 90.741155 \nL 237.912826 126.818306 \nL 238.004526 122.308662 \nL 238.096227 123.06027 \nL 238.187928 126.066699 \nL 238.37133 138.092416 \nL 238.463031 139.595631 \nL 238.646433 165.15028 \nL 238.829835 122.308662 \nL 238.921536 157.634207 \nL 239.013236 144.856882 \nL 239.196638 182.437249 \nL 239.38004 133.582772 \nL 239.471741 156.130992 \nL 239.838545 132.079558 \nL 239.930245 138.092416 \nL 240.113647 168.908317 \nL 240.205348 170.411531 \nL 240.38875 117.047411 \nL 240.480451 120.05384 \nL 240.572152 174.169568 \nL 240.663853 169.659924 \nL 240.847254 147.111704 \nL 241.030656 192.208144 \nL 241.214058 168.156709 \nL 241.305759 125.315092 \nL 241.39746 126.066699 \nL 241.489161 144.105275 \nL 241.580862 142.60206 \nL 241.672563 144.105275 \nL 241.764264 162.143851 \nL 241.947665 144.856882 \nL 242.039366 163.647065 \nL 242.314469 152.372955 \nL 242.40617 194.462966 \nL 242.681273 177.175997 \nL 242.772973 171.163139 \nL 242.956375 183.940463 \nL 243.139777 146.360097 \nL 243.231478 155.379385 \nL 243.41488 193.711358 \nL 243.598282 147.863311 \nL 243.689983 174.169568 \nL 243.965085 144.105275 \nL 244.056786 167.405102 \nL 244.148487 162.143851 \nL 244.240188 166.653495 \nL 244.331889 164.398673 \nL 244.42359 203.482254 \nL 244.973795 148.614919 \nL 245.065496 149.366526 \nL 245.248898 142.60206 \nL 245.340599 154.627777 \nL 245.4323 151.621348 \nL 245.524001 153.87617 \nL 245.615701 147.111704 \nL 245.707402 174.921175 \nL 245.799103 147.863311 \nL 245.890804 149.366526 \nL 245.982505 177.927605 \nL 246.165907 158.385814 \nL 246.257608 162.143851 \nL 246.44101 126.066699 \nL 246.532711 140.347238 \nL 246.716112 183.188856 \nL 246.807813 182.437249 \nL 246.899514 154.627777 \nL 246.991215 176.42439 \nL 247.082916 144.105275 \nL 247.174617 146.360097 \nL 247.358019 135.085987 \nL 247.44972 150.118133 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115.544196 \nL 252.218167 140.347238 \nL 252.309867 138.844024 \nL 252.401568 129.824736 \nL 252.493269 136.589202 \nL 252.58497 132.831165 \nL 252.676671 145.608489 \nL 252.951774 113.289374 \nL 253.043475 141.098845 \nL 253.135176 116.295804 \nL 253.226877 141.850453 \nL 253.318577 129.073128 \nL 253.410278 140.347238 \nL 253.685381 41.886678 \nL 253.868783 142.60206 \nL 254.052185 123.811877 \nL 254.143886 132.079558 \nL 254.327287 104.270086 \nL 254.510689 138.844024 \nL 254.694091 117.047411 \nL 254.877493 143.353667 \nL 255.244296 33.618998 \nL 255.427698 134.33438 \nL 255.519399 149.366526 \nL 255.6111 114.792589 \nL 255.794502 140.347238 \nL 255.977904 128.321521 \nL 256.069605 139.595631 \nL 256.161305 110.282945 \nL 256.253006 112.537767 \nL 256.528109 153.124563 \nL 256.61981 144.105275 \nL 256.711511 119.302233 \nL 256.894913 132.079558 \nL 256.986614 129.824736 \nL 257.261716 100.51205 \nL 257.353417 110.282945 \nL 257.62852 81.721867 \nL 257.720221 60.676861 \nL 257.903623 120.805448 \nL 257.995324 132.831165 \nL 258.087024 118.550626 \nL 258.178725 119.302233 \nL 258.270426 130.576343 \nL 258.362127 129.073128 \nL 258.453828 130.576343 \nL 258.63723 119.302233 \nL 258.728931 92.995976 \nL 258.820632 108.028123 \nL 258.912333 107.276516 \nL 259.004033 114.792589 \nL 259.095734 89.23794 \nL 259.370837 113.289374 \nL 259.462538 102.015264 \nL 259.554239 112.537767 \nL 259.829342 74.205793 \nL 259.921043 90.741155 \nL 260.196145 77.212223 \nL 260.287846 46.396322 \nL 260.471248 57.670432 \nL 260.65465 98.257228 \nL 260.746351 89.989547 \nL 260.929752 97.50562 \nL 261.113154 109.531338 \nL 261.204855 97.50562 \nL 261.388257 127.569914 \nL 261.479958 120.05384 \nL 261.846761 38.880249 \nL 262.030163 108.77973 \nL 262.121864 102.015264 \nL 262.213565 105.773301 \nL 262.305266 101.263657 \nL 262.488668 114.040982 \nL 262.580369 145.608489 \nL 262.763771 101.263657 \nL 262.855471 123.811877 \nL 263.130574 90.741155 \nL 263.405677 126.066699 \nL 263.589079 92.995976 \nL 263.77248 113.289374 \nL 264.047583 92.995976 \nL 264.139284 92.995976 \nL 264.230985 114.792589 \nL 264.414387 76.460615 \nL 264.68949 121.557055 \nL 264.78119 97.50562 \nL 265.056293 119.302233 \nL 265.239695 88.486333 \nL 265.331396 89.23794 \nL 265.423097 92.995976 \nL 265.514798 105.773301 \nL 265.606499 139.595631 \nL 265.698199 120.05384 \nL 265.881601 126.066699 \nL 266.156704 96.754013 \nL 266.248405 99.760442 \nL 266.431807 111.78616 \nL 266.615208 97.50562 \nL 266.79861 110.282945 \nL 266.982012 89.23794 \nL 267.073713 98.257228 \nL 267.348816 77.96383 \nL 267.440517 93.747584 \nL 267.532218 90.741155 \nL 267.623918 105.021694 \nL 267.715619 91.492762 \nL 267.80732 112.537767 \nL 267.899021 95.250798 \nL 267.990722 125.315092 \nL 268.082423 104.270086 \nL 268.265825 165.15028 \nL 268.357526 155.379385 \nL 268.540927 96.754013 \nL 268.632628 100.51205 \nL 268.724329 95.250798 \nL 268.907731 152.372955 \nL 268.999432 150.118133 \nL 269.091133 119.302233 \nL 269.182834 135.837594 \nL 269.274535 124.563484 \nL 269.366236 131.32795 \nL 269.457937 117.047411 \nL 269.549637 121.557055 \nL 269.641338 114.792589 \nL 269.733039 95.250798 \nL 269.82474 124.563484 \nL 269.916441 111.78616 \nL 270.008142 82.473474 \nL 270.191544 111.78616 \nL 270.283245 100.51205 \nL 270.374946 105.773301 \nL 270.558347 98.257228 \nL 270.650048 91.492762 \nL 270.83345 120.05384 \nL 270.925151 112.537767 \nL 271.108553 132.079558 \nL 271.200254 124.563484 \nL 271.291955 163.647065 \nL 271.475356 116.295804 \nL 271.567057 113.289374 \nL 271.658758 126.818306 \nL 271.750459 115.544196 \nL 272.117263 153.124563 \nL 272.300665 137.340809 \nL 272.392365 153.87617 \nL 272.484066 149.366526 \nL 272.575767 120.05384 \nL 272.942571 167.405102 \nL 273.401075 120.05384 \nL 273.492776 138.092416 \nL 273.584477 131.32795 \nL 273.676178 149.366526 \nL 273.85958 141.850453 \nL 274.042982 177.175997 \nL 274.134683 165.901887 \nL 274.226384 123.811877 \nL 274.501486 193.711358 \nL 274.593187 186.946892 \nL 274.684888 163.647065 \nL 274.776589 165.15028 \nL 275.051692 155.379385 \nL 275.143393 135.085987 \nL 275.326794 164.398673 \nL 275.510196 139.595631 \nL 275.601897 164.398673 \nL 275.693598 144.105275 \nL 275.785299 144.856882 \nL 275.968701 171.163139 \nL 276.060402 177.927605 \nL 276.152102 177.175997 \nL 276.427205 117.047411 \nL 276.518906 129.073128 \nL 276.610607 163.647065 \nL 276.702308 157.634207 \nL 276.794009 121.557055 \nL 276.88571 161.392243 \nL 276.977411 158.385814 \nL 277.069112 139.595631 \nL 277.160812 174.921175 \nL 277.619317 143.353667 \nL 277.711018 172.666353 \nL 277.986121 150.869741 \nL 278.077821 153.124563 \nL 278.169522 150.869741 \nL 278.352924 141.850453 \nL 278.444625 161.392243 \nL 278.719728 141.098845 \nL 278.811429 153.87617 \nL 278.994831 139.595631 \nL 279.086531 176.42439 \nL 279.269933 162.895458 \nL 279.361634 163.647065 \nL 279.545036 146.360097 \nL 279.636737 185.443678 \nL 279.728438 178.679212 \nL 280.00354 123.811877 \nL 280.095241 121.557055 \nL 280.186942 139.595631 \nL 280.278643 138.844024 \nL 280.370344 141.850453 \nL 280.462045 126.818306 \nL 280.553746 155.379385 \nL 280.645447 150.118133 \nL 280.828849 171.163139 \nL 281.01225 135.085987 \nL 281.103951 164.398673 \nL 281.287353 141.850453 \nL 281.379054 147.111704 \nL 281.562456 100.51205 \nL 281.837559 173.417961 \nL 281.929259 144.105275 \nL 282.02096 148.614919 \nL 282.112661 174.921175 \nL 282.296063 100.51205 \nL 282.571166 163.647065 \nL 282.662867 179.430819 \nL 282.754568 175.672783 \nL 282.846268 163.647065 \nL 282.937969 134.33438 \nL 283.02967 138.844024 \nL 283.213072 141.098845 \nL 283.304773 173.417961 \nL 283.488175 89.989547 \nL 283.671577 153.124563 \nL 283.763278 131.32795 \nL 283.854978 133.582772 \nL 283.946679 148.614919 \nL 284.03838 133.582772 \nL 284.130081 149.366526 \nL 284.221782 121.557055 \nL 284.313483 147.111704 \nL 284.496885 104.270086 \nL 284.771987 169.659924 \nL 284.863688 119.302233 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295.592694 93.747584 \nL 295.684395 106.524908 \nL 295.776096 92.244369 \nL 295.867797 96.754013 \nL 296.051199 115.544196 \nL 296.2346 75.709008 \nL 296.418002 99.760442 \nL 296.509703 95.250798 \nL 296.601404 100.51205 \nL 296.876507 68.944542 \nL 296.968208 68.944542 \nL 297.059909 68.192935 \nL 297.151609 60.676861 \nL 297.335011 102.015264 \nL 297.426712 93.747584 \nL 297.610114 117.047411 \nL 297.793516 81.721867 \nL 297.885217 115.544196 \nL 298.25202 49.402751 \nL 298.435422 67.441327 \nL 298.527123 62.180076 \nL 298.618824 77.212223 \nL 298.710525 72.702579 \nL 298.893927 53.912395 \nL 299.077328 80.970259 \nL 299.169029 81.721867 \nL 299.26073 118.550626 \nL 299.352431 101.263657 \nL 299.444132 102.015264 \nL 299.535833 103.518479 \nL 299.627534 124.563484 \nL 299.719235 120.805448 \nL 299.994337 84.728296 \nL 300.177739 90.741155 \nL 300.452842 144.105275 \nL 300.544543 143.353667 \nL 300.636244 126.066699 \nL 300.819646 141.850453 \nL 301.094748 101.263657 \nL 301.27815 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118.550626 \nL 213.612086 97.50562 \nL 213.703787 116.295804 \nL 213.795488 100.51205 \nL 213.97889 120.805448 \nL 214.070591 105.021694 \nL 214.162291 136.589202 \nL 214.253992 110.282945 \nL 214.345693 125.315092 \nL 214.437394 113.289374 \nL 214.529095 141.098845 \nL 214.712497 53.160788 \nL 214.804198 68.192935 \nL 214.895899 89.23794 \nL 214.9876 71.199364 \nL 215.171001 147.111704 \nL 215.262702 139.595631 \nL 215.354403 105.021694 \nL 215.446104 120.805448 \nL 215.721207 47.899537 \nL 215.99631 141.098845 \nL 216.271412 59.173647 \nL 216.454814 115.544196 \nL 216.729917 85.479903 \nL 216.821618 114.040982 \nL 216.913319 108.028123 \nL 217.005019 107.276516 \nL 217.09672 138.092416 \nL 217.188421 136.589202 \nL 217.280122 122.308662 \nL 217.371823 125.315092 \nL 217.463524 130.576343 \nL 217.555225 150.869741 \nL 217.738627 121.557055 \nL 217.830328 117.799018 \nL 217.922029 138.844024 \nL 218.013729 102.015264 \nL 218.197131 121.557055 \nL 218.380533 93.747584 \nL 218.472234 68.192935 \nL 218.655636 144.856882 \nL 218.747337 138.844024 \nL 218.839038 159.137421 \nL 218.930738 150.118133 \nL 219.022439 156.130992 \nL 219.11414 146.360097 \nL 219.297542 90.741155 \nL 219.572645 162.895458 \nL 219.847748 133.582772 \nL 220.031149 167.405102 \nL 220.214551 111.034552 \nL 220.489654 138.844024 \nL 220.673056 173.417961 \nL 220.948158 133.582772 \nL 221.039859 130.576343 \nL 221.13156 146.360097 \nL 221.223261 186.946892 \nL 221.314962 180.182427 \nL 221.406663 165.15028 \nL 221.590065 100.51205 \nL 221.681766 157.634207 \nL 221.773466 151.621348 \nL 221.865167 169.659924 \nL 222.14027 131.32795 \nL 222.415373 109.531338 \nL 222.598775 128.321521 \nL 222.690476 162.143851 \nL 222.782176 161.392243 \nL 222.873877 147.111704 \nL 223.057279 195.96618 \nL 223.14898 214.756364 \nL 223.424083 171.914746 \nL 223.515784 197.469395 \nL 223.699185 153.124563 \nL 223.790886 162.895458 \nL 223.882587 159.889029 \nL 223.974288 169.659924 \nL 224.15769 157.634207 \nL 224.341092 154.627777 \nL 224.432793 163.647065 \nL 224.524494 159.889029 \nL 224.616195 168.156709 \nL 224.707895 162.895458 \nL 224.799596 147.863311 \nL 224.982998 204.985468 \nL 225.074699 208.743505 \nL 225.349802 156.882599 \nL 225.441503 147.111704 \nL 225.624904 202.730646 \nL 225.900007 185.443678 \nL 226.083409 156.130992 \nL 226.266811 196.717788 \nL 226.358512 193.711358 \nL 226.450213 184.692071 \nL 226.633614 156.130992 \nL 226.817016 189.953322 \nL 226.908717 177.175997 \nL 227.000418 186.946892 \nL 227.092119 185.443678 \nL 227.18382 175.672783 \nL 227.275521 213.253149 \nL 227.367222 208.743505 \nL 227.458923 207.991898 \nL 227.734025 143.353667 \nL 227.825726 147.111704 \nL 227.917427 188.450107 \nL 228.009128 180.934034 \nL 228.375932 141.850453 \nL 228.467632 152.372955 \nL 228.559333 146.360097 \nL 228.742735 198.221002 \nL 228.834436 180.934034 \nL 229.017838 186.195285 \nL 229.20124 128.321521 \nL 229.292941 138.092416 \nL 229.384642 155.379385 \nL 229.568043 143.353667 \nL 229.659744 169.659924 \nL 229.843146 145.608489 \nL 229.934847 182.437249 \nL 230.20995 115.544196 \nL 230.393351 176.42439 \nL 230.485052 123.811877 \nL 230.576753 130.576343 \nL 230.760155 180.182427 \nL 230.851856 162.143851 \nL 230.943557 108.028123 \nL 231.035258 119.302233 \nL 231.21866 184.692071 \nL 231.402061 135.837594 \nL 231.585463 180.934034 \nL 231.677164 153.124563 \nL 231.768865 182.437249 \nL 231.860566 141.098845 \nL 232.043968 177.175997 \nL 232.22737 147.111704 \nL 232.31907 187.6985 \nL 232.685874 102.015264 \nL 232.869276 171.914746 \nL 233.052678 184.692071 \nL 233.32778 150.869741 \nL 233.419481 128.321521 \nL 233.511182 156.882599 \nL 233.602883 145.608489 \nL 233.877986 167.405102 \nL 233.969687 150.118133 \nL 234.061388 168.908317 \nL 234.153089 115.544196 \nL 234.33649 179.430819 \nL 234.428191 171.163139 \nL 234.519892 102.766872 \nL 234.703294 150.118133 \nL 234.794995 144.105275 \nL 234.886696 171.914746 \nL 235.070098 116.295804 \nL 235.253499 153.124563 \nL 235.3452 141.098845 \nL 235.528602 171.163139 \nL 235.620303 141.098845 \nL 235.712004 155.379385 \nL 235.987107 135.085987 \nL 236.078807 154.627777 \nL 236.170508 138.092416 \nL 236.262209 101.263657 \nL 236.35391 110.282945 \nL 236.537312 147.111704 \nL 236.629013 115.544196 \nL 236.720714 162.143851 \nL 236.812415 135.085987 \nL 236.904116 162.895458 \nL 237.270919 81.721867 \nL 237.36262 94.499191 \nL 237.546022 135.837594 \nL 237.637723 106.524908 \nL 237.821125 147.111704 \nL 238.004526 105.773301 \nL 238.096227 79.467045 \nL 238.279629 134.33438 \nL 238.463031 149.366526 \nL 238.646433 120.05384 \nL 238.738134 137.340809 \nL 238.921536 94.499191 \nL 239.013236 96.002406 \nL 239.104937 123.811877 \nL 239.196638 120.805448 \nL 239.288339 123.06027 \nL 239.471741 93.747584 \nL 239.563442 98.257228 \nL 239.655143 137.340809 \nL 239.746844 135.837594 \nL 239.930245 125.315092 \nL 240.021946 117.047411 \nL 240.205348 135.085987 \nL 240.38875 117.047411 \nL 240.480451 123.06027 \nL 240.572152 120.05384 \nL 240.663853 74.205793 \nL 240.755554 100.51205 \nL 240.847254 99.760442 \nL 240.938955 110.282945 \nL 241.030656 96.002406 \nL 241.214058 117.047411 \nL 241.305759 111.78616 \nL 241.489161 133.582772 \nL 241.580862 97.50562 \nL 241.672563 99.760442 \nL 241.855964 117.047411 \nL 242.039366 92.244369 \nL 242.131067 96.002406 \nL 242.222768 81.721867 \nL 242.314469 92.244369 \nL 242.40617 76.460615 \nL 242.589572 132.831165 \nL 242.681273 129.073128 \nL 242.772973 103.518479 \nL 242.864674 123.811877 \nL 242.956375 118.550626 \nL 243.048076 92.995976 \nL 243.139777 98.257228 \nL 243.41488 146.360097 \nL 243.689983 119.302233 \nL 243.781683 119.302233 \nL 243.873384 128.321521 \nL 243.965085 111.034552 \nL 244.056786 114.792589 \nL 244.148487 127.569914 \nL 244.240188 99.008835 \nL 244.331889 121.557055 \nL 244.42359 87.734725 \nL 244.606992 135.085987 \nL 244.698692 97.50562 \nL 244.790393 134.33438 \nL 245.065496 107.276516 \nL 245.157197 109.531338 \nL 245.248898 78.715437 \nL 245.340599 84.728296 \nL 245.4323 117.047411 \nL 245.524001 94.499191 \nL 245.615701 102.766872 \nL 245.707402 92.995976 \nL 245.890804 45.644715 \nL 246.074206 95.250798 \nL 246.165907 88.486333 \nL 246.349309 118.550626 \nL 246.44101 109.531338 \nL 246.624411 53.160788 \nL 246.807813 112.537767 \nL 246.899514 105.773301 \nL 246.991215 108.028123 \nL 247.082916 96.754013 \nL 247.174617 66.68972 \nL 247.358019 106.524908 \nL 247.633121 61.428469 \nL 247.816523 65.186505 \nL 247.908224 49.402751 \nL 247.999925 60.676861 \nL 248.091626 48.651144 \nL 248.183327 59.925254 \nL 248.275028 102.015264 \nL 248.45843 53.160788 \nL 248.641831 108.77973 \nL 248.733532 105.773301 \nL 248.825233 56.167217 \nL 249.008635 100.51205 \nL 249.100336 116.295804 \nL 249.192037 115.544196 \nL 249.283738 120.805448 \nL 249.467139 82.473474 \nL 249.55884 98.257228 \nL 249.650541 89.23794 \nL 249.742242 92.244369 \nL 249.925644 119.302233 \nL 250.017345 139.595631 \nL 250.200747 120.05384 \nL 250.384149 139.595631 \nL 250.475849 110.282945 \nL 250.56755 114.040982 \nL 250.659251 120.805448 \nL 250.750952 118.550626 \nL 250.842653 156.130992 \nL 250.934354 131.32795 \nL 251.026055 134.33438 \nL 251.209457 164.398673 \nL 251.301158 171.914746 \nL 251.57626 98.257228 \nL 251.667961 131.32795 \nL 251.759662 126.818306 \nL 251.851363 128.321521 \nL 252.034765 168.156709 \nL 252.126466 164.398673 \nL 252.309867 148.614919 \nL 252.401568 154.627777 \nL 252.676671 90.741155 \nL 252.860073 135.837594 \nL 253.043475 117.047411 \nL 253.135176 149.366526 \nL 253.501979 113.289374 \nL 253.59368 111.78616 \nL 253.685381 113.289374 \nL 253.777082 134.33438 \nL 253.868783 117.047411 \nL 253.960484 127.569914 \nL 254.052185 117.047411 \nL 254.143886 130.576343 \nL 254.235586 113.289374 \nL 254.327287 117.799018 \nL 254.418988 163.647065 \nL 254.60239 105.773301 \nL 254.877493 180.182427 \nL 254.969194 177.927605 \nL 255.152596 152.372955 \nL 255.335997 168.156709 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151.621348 \nL 260.287846 165.901887 \nL 260.379547 155.379385 \nL 260.471248 183.940463 \nL 260.65465 158.385814 \nL 260.838052 195.96618 \nL 261.021453 165.15028 \nL 261.113154 214.756364 \nL 261.204855 209.495112 \nL 261.388257 122.308662 \nL 261.479958 145.608489 \nL 261.571659 142.60206 \nL 261.66336 143.353667 \nL 261.755061 139.595631 \nL 261.846761 156.882599 \nL 261.938462 154.627777 \nL 262.121864 152.372955 \nL 262.213565 180.934034 \nL 262.580369 135.837594 \nL 262.67207 134.33438 \nL 262.763771 140.347238 \nL 262.947172 171.163139 \nL 263.222275 107.276516 \nL 263.497378 192.208144 \nL 263.589079 175.672783 \nL 263.77248 131.32795 \nL 263.864181 135.837594 \nL 263.955882 147.111704 \nL 264.047583 117.047411 \nL 264.139284 166.653495 \nL 264.230985 151.621348 \nL 264.322686 164.398673 \nL 264.506088 130.576343 \nL 264.597789 139.595631 \nL 264.68949 138.844024 \nL 264.872891 132.831165 \nL 264.964592 171.914746 \nL 265.147994 136.589202 \nL 265.331396 123.06027 \nL 265.698199 173.417961 \nL 265.7899 161.392243 \nL 265.881601 165.901887 \nL 265.973302 182.437249 \nL 266.065003 177.175997 \nL 266.156704 130.576343 \nL 266.248405 158.385814 \nL 266.431807 112.537767 \nL 266.523508 152.372955 \nL 266.615208 150.869741 \nL 266.706909 117.799018 \nL 266.982012 188.450107 \nL 267.165414 99.008835 \nL 267.348816 142.60206 \nL 267.440517 144.856882 \nL 267.532218 110.282945 \nL 267.623918 156.882599 \nL 267.715619 143.353667 \nL 267.899021 162.895458 \nL 267.990722 163.647065 \nL 268.082423 171.163139 \nL 268.174124 169.659924 \nL 268.632628 92.995976 \nL 268.81603 126.066699 \nL 268.999432 139.595631 \nL 269.091133 123.06027 \nL 269.182834 147.863311 \nL 269.274535 137.340809 \nL 269.366236 158.385814 \nL 269.549637 120.05384 \nL 269.641338 117.799018 \nL 269.733039 126.818306 \nL 269.82474 109.531338 \nL 270.008142 147.111704 \nL 270.099843 145.608489 \nL 270.191544 141.098845 \nL 270.283245 126.066699 \nL 270.374946 135.085987 \nL 270.466646 120.05384 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105.773301 \nL 280.737148 90.741155 \nL 281.01225 126.818306 \nL 281.103951 101.263657 \nL 281.195652 130.576343 \nL 281.287353 113.289374 \nL 281.379054 120.05384 \nL 281.470755 148.614919 \nL 281.745858 105.773301 \nL 281.837559 68.192935 \nL 282.02096 111.034552 \nL 282.112661 135.837594 \nL 282.204362 111.034552 \nL 282.296063 129.073128 \nL 282.387764 97.50562 \nL 282.479465 131.32795 \nL 282.662867 108.028123 \nL 282.754568 132.831165 \nL 282.846268 108.028123 \nL 282.937969 111.034552 \nL 283.02967 101.263657 \nL 283.213072 123.811877 \nL 283.488175 80.970259 \nL 283.579876 144.105275 \nL 283.671577 138.092416 \nL 283.763278 159.137421 \nL 283.854978 149.366526 \nL 284.03838 99.760442 \nL 284.221782 141.850453 \nL 284.313483 137.340809 \nL 284.496885 153.124563 \nL 284.771987 120.805448 \nL 284.863688 147.111704 \nL 284.955389 141.850453 \nL 285.04709 138.844024 \nL 285.230492 124.563484 \nL 285.413894 133.582772 \nL 285.505595 118.550626 \nL 285.597296 141.098845 \nL 285.688996 111.78616 \nL 285.780697 132.079558 \nL 285.872398 115.544196 \nL 285.964099 117.047411 \nL 286.0558 138.092416 \nL 286.147501 115.544196 \nL 286.239202 144.856882 \nL 286.330903 131.32795 \nL 286.514305 149.366526 \nL 286.697706 120.805448 \nL 286.789407 165.901887 \nL 287.06451 104.270086 \nL 287.339613 189.953322 \nL 287.431314 188.450107 \nL 287.523015 171.914746 \nL 287.614715 173.417961 \nL 287.889818 140.347238 \nL 287.981519 177.927605 \nL 288.07322 167.405102 \nL 288.164921 178.679212 \nL 288.531725 144.105275 \nL 288.623425 149.366526 \nL 288.715126 143.353667 \nL 288.806827 123.811877 \nL 288.990229 144.856882 \nL 289.173631 154.627777 \nL 289.265332 141.098845 \nL 289.357033 168.156709 \nL 289.448734 159.889029 \nL 289.540434 132.831165 \nL 289.723836 149.366526 \nL 289.815537 147.111704 \nL 289.998939 121.557055 \nL 290.182341 160.640636 \nL 290.274042 131.32795 \nL 290.365743 144.856882 \nL 290.457443 138.844024 \nL 290.549144 185.443678 \nL 290.640845 177.175997 \nL 290.732546 153.124563 \nL 290.824247 193.711358 \nL 290.915948 182.437249 \nL 291.09935 131.32795 \nL 291.191051 179.430819 \nL 291.282752 174.921175 \nL 291.374453 139.595631 \nL 291.557854 198.221002 \nL 291.741256 152.372955 \nL 291.832957 150.118133 \nL 291.924658 138.844024 \nL 292.10806 160.640636 \nL 292.474863 144.105275 \nL 292.566564 156.130992 \nL 292.749966 196.717788 \nL 292.841667 185.443678 \nL 292.933368 204.985468 \nL 293.025069 198.97261 \nL 293.11677 159.137421 \nL 293.208471 160.640636 \nL 293.391872 147.863311 \nL 293.483573 148.614919 \nL 293.575274 154.627777 \nL 293.758676 214.004756 \nL 293.850377 207.991898 \nL 293.942078 156.130992 \nL 294.033779 160.640636 \nL 294.12548 154.627777 \nL 294.217181 180.182427 \nL 294.308881 175.672783 \nL 294.492283 163.647065 \nL 294.583984 153.87617 \nL 294.675685 158.385814 \nL 294.859087 180.182427 \nL 295.042489 141.850453 \nL 295.13419 162.143851 \nL 295.317591 135.085987 \nL 295.409292 128.321521 \nL 295.500993 138.092416 \nL 295.592694 131.32795 \nL 295.684395 132.079558 \nL 295.776096 147.863311 \nL 295.959498 126.818306 \nL 296.051199 127.569914 \nL 296.2346 167.405102 \nL 296.326301 149.366526 \nL 296.418002 150.869741 \nL 296.509703 150.869741 \nL 296.601404 154.627777 \nL 296.693105 169.659924 \nL 296.876507 150.869741 \nL 296.968208 156.882599 \nL 297.151609 147.111704 \nL 297.335011 163.647065 \nL 297.426712 144.856882 \nL 297.518413 164.398673 \nL 297.610114 147.111704 \nL 297.793516 167.405102 \nL 297.885217 155.379385 \nL 297.976918 175.672783 \nL 298.160319 129.824736 \nL 298.25202 145.608489 \nL 298.343721 129.824736 \nL 298.435422 162.143851 \nL 298.527123 154.627777 \nL 298.618824 180.182427 \nL 298.802226 143.353667 \nL 298.893927 144.105275 \nL 298.985628 135.837594 \nL 299.077328 141.850453 \nL 299.169029 177.927605 \nL 299.26073 154.627777 \nL 299.444132 173.417961 \nL 299.627534 126.818306 \nL 299.810936 147.863311 \nL 299.902637 129.824736 \nL 300.086038 168.156709 \nL 300.177739 165.15028 \nL 300.26944 146.360097 \nL 300.361141 168.908317 \nL 300.452842 158.385814 \nL 300.544543 134.33438 \nL 300.727945 173.417961 \nL 300.819646 164.398673 \nL 300.911347 183.188856 \nL 301.094748 92.244369 \nL 301.27815 137.340809 \nL 301.461552 156.882599 \nL 301.553253 94.499191 \nL 301.644954 105.021694 \nL 301.828356 153.87617 \nL 302.011757 85.479903 \nL 302.195159 149.366526 \nL 302.378561 178.679212 \nL 302.653664 141.850453 \nL 302.745365 140.347238 \nL 302.837066 165.901887 \nL 302.928766 141.098845 \nL 303.020467 77.96383 \nL 303.203869 146.360097 \nL 303.29557 142.60206 \nL 303.387271 113.289374 \nL 303.570673 139.595631 \nL 303.662374 150.869741 \nL 303.845775 89.989547 \nL 303.937476 127.569914 \nL 304.029177 123.06027 \nL 304.212579 145.608489 \nL 304.30428 140.347238 \nL 304.487682 97.50562 \nL 304.579383 71.950971 \nL 304.762784 123.06027 \nL 304.854485 124.563484 \nL 304.946186 131.32795 \nL 305.037887 126.066699 \nL 305.129588 157.634207 \nL 305.221289 117.047411 \nL 305.31299 119.302233 \nL 305.404691 94.499191 \nL 305.588093 108.028123 \nL 305.771494 148.614919 \nL 305.863195 127.569914 \nL 305.954896 150.118133 \nL 306.138298 32.115783 \nL 306.3217 133.582772 \nL 306.413401 124.563484 \nL 306.505102 132.079558 \nL 306.596803 120.05384 \nL 306.780204 146.360097 \nL 306.963606 117.047411 \nL 307.055307 118.550626 \nL 307.147008 140.347238 \nL 307.238709 127.569914 \nL 307.33041 135.837594 \nL 307.422111 95.250798 \nL 307.513812 123.06027 \nL 307.605513 117.047411 \nL 307.880615 129.073128 \nL 307.972316 123.811877 \nL 308.064017 88.486333 \nL 308.247419 129.824736 \nL 308.33912 136.589202 \nL 308.430821 108.028123 \nL 308.522522 129.073128 \nL 308.705923 90.741155 \nL 308.889325 123.06027 \nL 308.981026 124.563484 \nL 309.072727 120.05384 \nL 309.256129 91.492762 \nL 309.439531 114.792589 \nL 309.531231 100.51205 \nL 309.714633 119.302233 \nL 309.806334 105.021694 \nL 309.898035 132.079558 \nL 309.989736 115.544196 \nL 310.081437 123.06027 \nL 310.173138 106.524908 \nL 310.264839 111.78616 \nL 310.35654 105.773301 \nL 310.448241 108.77973 \nL 310.539941 106.524908 \nL 310.631642 66.68972 \nL 310.906745 126.066699 \nL 310.998446 124.563484 \nL 311.090147 129.073128 \nL 311.181848 106.524908 \nL 311.273549 121.557055 \nL 311.45695 97.50562 \nL 311.548651 100.51205 \nL 311.640352 118.550626 \nL 311.732053 114.792589 \nL 311.823754 83.225081 \nL 312.007156 113.289374 \nL 312.098857 89.23794 \nL 312.282259 102.766872 \nL 312.37396 138.092416 \nL 312.557361 71.950971 \nL 312.649062 96.754013 \nL 312.740763 79.467045 \nL 312.924165 110.282945 \nL 313.015866 117.047411 \nL 313.107567 99.760442 \nL 313.199268 107.276516 \nL 313.382669 94.499191 \nL 313.47437 102.766872 \nL 313.566071 131.32795 \nL 313.657772 103.518479 \nL 313.932875 132.831165 \nL 314.207978 78.715437 \nL 314.391379 137.340809 \nL 314.574781 111.034552 \nL 314.666482 137.340809 \nL 314.758183 132.079558 \nL 314.941585 98.257228 \nL 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138.844024 \nL 320.627041 154.627777 \nL 320.902144 99.008835 \nL 320.993844 147.111704 \nL 321.360648 114.040982 \nL 321.54405 164.398673 \nL 321.727452 133.582772 \nL 321.910854 180.934034 \nL 322.002554 157.634207 \nL 322.094255 162.895458 \nL 322.277657 150.869741 \nL 322.369358 173.417961 \nL 322.461059 143.353667 \nL 322.644461 174.169568 \nL 322.736162 173.417961 \nL 323.011264 114.040982 \nL 323.194666 138.844024 \nL 323.286367 182.437249 \nL 323.378068 173.417961 \nL 323.469769 181.685641 \nL 323.744872 153.124563 \nL 323.836572 153.124563 \nL 323.928273 183.188856 \nL 324.111675 139.595631 \nL 324.203376 148.614919 \nL 324.295077 165.15028 \nL 324.478479 138.844024 \nL 324.57018 161.392243 \nL 324.661881 156.882599 \nL 324.753582 150.869741 \nL 324.936983 162.895458 \nL 325.028684 151.621348 \nL 325.212086 167.405102 \nL 325.303787 210.24672 \nL 325.395488 202.730646 \nL 325.57889 152.372955 \nL 325.670591 154.627777 \nL 325.853992 135.085987 \nL 325.945693 136.589202 \nL 326.037394 127.569914 \nL 326.129095 59.173647 \nL 326.220796 80.218652 \nL 326.312497 73.454186 \nL 326.404198 105.021694 \nL 326.5876 96.002406 \nL 326.679301 96.002406 \nL 326.771001 83.976689 \nL 326.862702 50.905966 \nL 327.046104 92.995976 \nL 327.137805 114.792589 \nL 327.412908 26.854532 \nL 327.59631 59.925254 \nL 327.68801 28.357746 \nL 327.871412 98.257228 \nL 327.963113 77.96383 \nL 328.054814 123.811877 \nL 328.421618 74.205793 \nL 328.513319 68.944542 \nL 328.788421 101.263657 \nL 328.880122 99.008835 \nL 328.971823 99.760442 \nL 329.155225 50.154359 \nL 329.522029 105.021694 \nL 329.613729 86.231511 \nL 329.70543 26.854532 \nL 329.888832 111.78616 \nL 329.980533 110.282945 \nL 330.255636 48.651144 \nL 330.347337 55.41561 \nL 330.622439 93.747584 \nL 330.71414 96.754013 \nL 330.805841 89.989547 \nL 330.897542 90.741155 \nL 331.080944 106.524908 \nL 331.172645 75.709008 \nL 331.264346 87.734725 \nL 331.356047 83.225081 \nL 331.447748 55.41561 \nL 331.539448 80.970259 \nL 331.631149 74.957401 \nL 331.906252 114.792589 \nL 331.997953 107.276516 \nL 332.089654 129.073128 \nL 332.181355 92.244369 \nL 332.273056 93.747584 \nL 332.364757 126.066699 \nL 332.456457 123.06027 \nL 332.548158 104.270086 \nL 332.73156 129.824736 \nL 332.823261 135.085987 \nL 332.914962 126.818306 \nL 333.006663 108.028123 \nL 333.098364 130.576343 \nL 333.190065 87.734725 \nL 333.281766 89.23794 \nL 333.465167 154.627777 \nL 333.556868 148.614919 \nL 333.648569 114.040982 \nL 333.74027 132.831165 \nL 333.831971 114.040982 \nL 333.923672 132.079558 \nL 334.107074 96.754013 \nL 334.198775 105.773301 \nL 334.382176 89.23794 \nL 334.473877 88.486333 \nL 334.565578 83.225081 \nL 334.657279 86.231511 \nL 334.74898 78.715437 \nL 334.840681 89.989547 \nL 334.932382 139.595631 \nL 335.115784 95.250798 \nL 335.299185 157.634207 \nL 335.482587 113.289374 \nL 335.574288 117.047411 \nL 335.665989 114.792589 \nL 335.75769 123.811877 \nL 335.849391 121.557055 \nL 336.032793 111.034552 \nL 336.216195 147.111704 \nL 336.491297 128.321521 \nL 336.674699 159.137421 \nL 336.7664 140.347238 \nL 336.858101 144.856882 \nL 336.949802 140.347238 \nL 337.041503 159.137421 \nL 337.133204 150.118133 \nL 337.316605 109.531338 \nL 337.408306 150.118133 \nL 337.500007 139.595631 \nL 337.591708 113.289374 \nL 337.958512 153.87617 \nL 338.141913 135.085987 \nL 338.233614 174.921175 \nL 338.417016 150.869741 \nL 338.508717 130.576343 \nL 338.600418 141.098845 \nL 338.875521 198.97261 \nL 339.058923 174.169568 \nL 339.242324 128.321521 \nL 339.425726 120.05384 \nL 339.517427 132.079558 \nL 339.609128 130.576343 \nL 339.79253 126.066699 \nL 339.884231 118.550626 \nL 340.159333 141.098845 \nL 340.251034 130.576343 \nL 340.342735 171.914746 \nL 340.434436 161.392243 \nL 340.526137 195.96618 \nL 340.709539 180.182427 \nL 340.80124 132.079558 \nL 340.892941 171.914746 \nL 341.168043 129.073128 \nL 341.443146 194.462966 \nL 341.534847 182.437249 \nL 341.626548 167.405102 \nL 341.718249 186.195285 \nL 341.80995 181.685641 \nL 341.901651 161.392243 \nL 341.993351 178.679212 \nL 342.451856 138.092416 \nL 342.635258 143.353667 \nL 342.726959 134.33438 \nL 342.81866 139.595631 \nL 342.91036 165.901887 \nL 343.002061 162.143851 \nL 343.185463 153.87617 \nL 343.277164 165.15028 \nL 343.460566 147.863311 \nL 343.552267 180.182427 \nL 343.643968 163.647065 \nL 343.735669 171.914746 \nL 343.82737 168.908317 \nL 344.010771 160.640636 \nL 344.102472 167.405102 \nL 344.194173 148.614919 \nL 344.285874 177.175997 \nL 344.560977 124.563484 \nL 344.744379 147.863311 \nL 344.836079 141.098845 \nL 344.92778 147.111704 \nL 345.019481 145.608489 \nL 345.477986 190.704929 \nL 345.753089 147.111704 \nL 345.844789 139.595631 \nL 345.93649 168.156709 \nL 346.028191 162.895458 \nL 346.119892 165.901887 \nL 346.303294 162.143851 \nL 346.486696 192.208144 \nL 346.761798 147.111704 \nL 346.853499 150.118133 \nL 347.036901 135.837594 \nL 347.128602 157.634207 \nL 347.312004 120.805448 \nL 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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "train.plot()\n",
    "val.plot()\n",
    "pred_val.plot()\n",
    "print(\"MAPE:\", mape(pred_val, val))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Improvement 1: Crop the training set\n",
    "The first improvement consists of cropping the training set before feeding it to the FFT algorithm such that the first timestamp in the cropped series matches the first timestamp to be predicted in terms of seasonality, i.e. it has the same month, day, weekday, time of day, etc. We can achieve this by passing the optional argument 'required_matches' to the FFT constructor that explicitly tells our model which timestamp attributes are relevant. If we don't set it manually, the model will attempt to automatically find the pd.Timestamp attributes that are relevant and crop the training set accordingly (which we will do here)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = FFT(nr_freqs_to_keep=None)\n",
    "model.fit(train)\n",
    "pred_val = model.predict(len(val))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the results look like the seasonality of the predictions nicely aligns with the seasonality of the validation set. However, we are still just repeating the training set, including all of the noise. Looking at the error we can see that this is still a pretty bad forecast."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "MAPE: 300841486646235.06\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
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125.315092 \nL 89.357361 117.047411 \nL 89.540763 135.085987 \nL 89.724165 117.047411 \nL 89.815866 123.06027 \nL 89.907567 120.05384 \nL 89.999268 74.205793 \nL 90.090969 100.51205 \nL 90.182669 99.760442 \nL 90.27437 110.282945 \nL 90.366071 96.002406 \nL 90.549473 117.047411 \nL 90.641174 111.78616 \nL 90.824576 133.582772 \nL 90.916277 97.50562 \nL 91.007978 99.760442 \nL 91.191379 117.047411 \nL 91.374781 92.244369 \nL 91.466482 96.002406 \nL 91.558183 81.721867 \nL 91.649884 92.244369 \nL 91.741585 76.460615 \nL 91.924987 132.831165 \nL 92.016688 129.073128 \nL 92.108388 103.518479 \nL 92.200089 123.811877 \nL 92.29179 118.550626 \nL 92.383491 92.995976 \nL 92.475192 98.257228 \nL 92.750295 146.360097 \nL 93.025397 119.302233 \nL 93.117098 119.302233 \nL 93.208799 128.321521 \nL 93.3005 111.034552 \nL 93.392201 114.792589 \nL 93.483902 127.569914 \nL 93.575603 99.008835 \nL 93.667304 121.557055 \nL 93.759005 87.734725 \nL 93.942407 135.085987 \nL 94.034107 97.50562 \nL 94.125808 134.33438 \nL 94.400911 107.276516 \nL 94.492612 109.531338 \nL 94.584313 78.715437 \nL 94.676014 84.728296 \nL 94.767715 117.047411 \nL 94.859416 94.499191 \nL 94.951116 102.766872 \nL 95.042817 92.995976 \nL 95.226219 45.644715 \nL 95.409621 95.250798 \nL 95.501322 88.486333 \nL 95.684724 118.550626 \nL 95.776425 109.531338 \nL 95.959826 53.160788 \nL 96.143228 112.537767 \nL 96.234929 105.773301 \nL 96.32663 108.028123 \nL 96.418331 96.754013 \nL 96.510032 66.68972 \nL 96.693434 106.524908 \nL 96.968536 61.428469 \nL 97.151938 65.186505 \nL 97.243639 49.402751 \nL 97.33534 60.676861 \nL 97.427041 48.651144 \nL 97.518742 59.925254 \nL 97.610443 102.015264 \nL 97.793844 53.160788 \nL 97.977246 108.77973 \nL 98.068947 105.773301 \nL 98.160648 56.167217 \nL 98.34405 100.51205 \nL 98.435751 116.295804 \nL 98.527452 115.544196 \nL 98.619153 120.805448 \nL 98.802554 82.473474 \nL 98.894255 98.257228 \nL 98.985956 89.23794 \nL 99.077657 92.244369 \nL 99.261059 119.302233 \nL 99.35276 139.595631 \nL 99.536162 120.05384 \nL 99.719563 139.595631 \nL 99.811264 110.282945 \nL 99.902965 114.040982 \nL 99.994666 120.805448 \nL 100.086367 118.550626 \nL 100.178068 156.130992 \nL 100.269769 131.32795 \nL 100.36147 134.33438 \nL 100.544872 164.398673 \nL 100.636572 171.914746 \nL 100.911675 98.257228 \nL 101.003376 131.32795 \nL 101.095077 126.818306 \nL 101.186778 128.321521 \nL 101.37018 168.156709 \nL 101.461881 164.398673 \nL 101.645282 148.614919 \nL 101.736983 154.627777 \nL 102.012086 90.741155 \nL 102.195488 135.837594 \nL 102.37889 117.047411 \nL 102.470591 149.366526 \nL 102.837394 113.289374 \nL 102.929095 111.78616 \nL 103.020796 113.289374 \nL 103.112497 134.33438 \nL 103.204198 117.047411 \nL 103.295899 127.569914 \nL 103.3876 117.047411 \nL 103.479301 130.576343 \nL 103.571001 113.289374 \nL 103.662702 117.799018 \nL 103.754403 163.647065 \nL 103.937805 105.773301 \nL 104.212908 180.182427 \nL 104.304609 177.927605 \nL 104.48801 152.372955 \nL 104.671412 168.156709 \nL 104.763113 156.130992 \nL 104.854814 115.544196 \nL 104.946515 125.315092 \nL 105.038216 165.901887 \nL 105.221618 123.811877 \nL 105.405019 158.385814 \nL 105.588421 132.079558 \nL 105.680122 133.582772 \nL 105.771823 174.921175 \nL 105.863524 157.634207 \nL 105.955225 172.666353 \nL 106.138627 142.60206 \nL 106.230328 162.143851 \nL 106.322029 152.372955 \nL 106.413729 156.130992 \nL 106.50543 179.430819 \nL 106.688832 160.640636 \nL 106.872234 143.353667 \nL 107.055636 192.208144 \nL 107.147337 203.482254 \nL 107.239038 195.96618 \nL 107.422439 127.569914 \nL 107.605841 165.15028 \nL 107.697542 154.627777 \nL 107.789243 155.379385 \nL 107.880944 189.953322 \nL 107.972645 185.443678 \nL 108.064346 169.659924 \nL 108.156047 184.692071 \nL 108.431149 141.098845 \nL 108.52285 143.353667 \nL 108.614551 160.640636 \nL 108.706252 153.87617 \nL 108.797953 154.627777 \nL 108.981355 148.614919 \nL 109.073056 152.372955 \nL 109.164757 196.717788 \nL 109.348158 170.411531 \nL 109.53156 151.621348 \nL 109.623261 165.901887 \nL 109.714962 155.379385 \nL 109.806663 183.940463 \nL 109.990065 158.385814 \nL 110.173466 195.96618 \nL 110.356868 165.15028 \nL 110.448569 214.756364 \nL 110.54027 209.495112 \nL 110.723672 122.308662 \nL 110.815373 145.608489 \nL 110.907074 142.60206 \nL 110.998775 143.353667 \nL 111.090476 139.595631 \nL 111.182176 156.882599 \nL 111.273877 154.627777 \nL 111.457279 152.372955 \nL 111.54898 180.934034 \nL 111.915784 135.837594 \nL 112.007485 134.33438 \nL 112.099185 140.347238 \nL 112.282587 171.163139 \nL 112.55769 107.276516 \nL 112.832793 192.208144 \nL 112.924494 175.672783 \nL 113.107895 131.32795 \nL 113.199596 135.837594 \nL 113.291297 147.111704 \nL 113.382998 117.047411 \nL 113.474699 166.653495 \nL 113.5664 151.621348 \nL 113.658101 164.398673 \nL 113.841503 130.576343 \nL 113.933204 139.595631 \nL 114.024904 138.844024 \nL 114.208306 132.831165 \nL 114.300007 171.914746 \nL 114.483409 136.589202 \nL 114.666811 123.06027 \nL 115.033614 173.417961 \nL 115.125315 161.392243 \nL 115.217016 165.901887 \nL 115.308717 182.437249 \nL 115.400418 177.175997 \nL 115.492119 130.576343 \nL 115.58382 158.385814 \nL 115.767222 112.537767 \nL 115.858923 152.372955 \nL 115.950623 150.869741 \nL 116.042324 117.799018 \nL 116.317427 188.450107 \nL 116.500829 99.008835 \nL 116.684231 142.60206 \nL 116.775932 144.856882 \nL 116.867632 110.282945 \nL 116.959333 156.882599 \nL 117.051034 143.353667 \nL 117.234436 162.895458 \nL 117.326137 163.647065 \nL 117.417838 171.163139 \nL 117.509539 169.659924 \nL 117.968043 92.995976 \nL 118.151445 126.066699 \nL 118.334847 139.595631 \nL 118.426548 123.06027 \nL 118.518249 147.863311 \nL 118.60995 137.340809 \nL 118.701651 158.385814 \nL 118.885052 120.05384 \nL 118.976753 117.799018 \nL 119.068454 126.818306 \nL 119.160155 109.531338 \nL 119.343557 147.111704 \nL 119.435258 145.608489 \nL 119.526959 141.098845 \nL 119.61866 126.066699 \nL 119.71036 135.085987 \nL 119.802061 120.05384 \nL 120.077164 158.385814 \nL 120.260566 103.518479 \nL 120.443968 156.882599 \nL 120.62737 133.582772 \nL 120.71907 133.582772 \nL 120.902472 115.544196 \nL 121.085874 171.914746 \nL 121.177575 141.098845 \nL 121.269276 159.889029 \nL 121.360977 133.582772 \nL 121.452678 139.595631 \nL 121.544379 92.995976 \nL 121.636079 102.015264 \nL 121.72778 105.773301 \nL 121.819481 95.250798 \nL 122.002883 108.028123 \nL 122.277986 82.473474 \nL 122.461388 129.073128 \nL 122.644789 115.544196 \nL 122.73649 124.563484 \nL 122.828191 99.760442 \nL 123.011593 123.811877 \nL 123.103294 111.034552 \nL 123.194995 132.831165 \nL 123.286696 124.563484 \nL 123.378397 90.741155 \nL 123.470098 102.015264 \nL 123.561798 130.576343 \nL 123.7452 102.015264 \nL 123.836901 103.518479 \nL 123.928602 102.015264 \nL 124.020303 114.792589 \nL 124.112004 61.428469 \nL 124.203705 79.467045 \nL 124.295406 123.06027 \nL 124.387107 89.23794 \nL 124.478807 111.034552 \nL 124.570508 83.225081 \nL 124.845611 131.32795 \nL 125.029013 61.428469 \nL 125.120714 79.467045 \nL 125.212415 68.192935 \nL 125.579218 132.079558 \nL 125.670919 92.244369 \nL 125.76262 93.747584 \nL 125.854321 117.047411 \nL 125.946022 114.040982 \nL 126.037723 100.51205 \nL 126.129424 120.805448 \nL 126.404526 74.957401 \nL 126.496227 79.467045 \nL 126.587928 77.96383 \nL 126.679629 129.073128 \nL 126.77133 125.315092 \nL 126.863031 123.06027 \nL 126.954732 103.518479 \nL 127.229835 135.837594 \nL 127.413236 73.454186 \nL 127.596638 130.576343 \nL 127.688339 135.085987 \nL 127.78004 104.270086 \nL 127.963442 123.811877 \nL 128.055143 104.270086 \nL 128.146844 131.32795 \nL 128.330245 97.50562 \nL 128.421946 108.028123 \nL 128.605348 79.467045 \nL 128.697049 102.015264 \nL 128.78875 95.250798 \nL 128.880451 98.257228 \nL 128.972152 96.002406 \nL 129.063853 89.989547 \nL 129.155554 112.537767 \nL 129.247254 111.034552 \nL 129.522357 89.989547 \nL 129.614058 107.276516 \nL 129.79746 72.702579 \nL 129.889161 74.205793 \nL 129.980862 105.773301 \nL 130.072563 90.741155 \nL 130.347665 126.818306 \nL 130.439366 101.263657 \nL 130.531067 130.576343 \nL 130.622768 113.289374 \nL 130.714469 120.05384 \nL 130.80617 148.614919 \nL 131.081273 105.773301 \nL 131.172973 68.192935 \nL 131.356375 111.034552 \nL 131.448076 135.837594 \nL 131.539777 111.034552 \nL 131.631478 129.073128 \nL 131.723179 97.50562 \nL 131.81488 131.32795 \nL 131.998282 108.028123 \nL 132.089983 132.831165 \nL 132.181683 108.028123 \nL 132.273384 111.034552 \nL 132.365085 101.263657 \nL 132.548487 123.811877 \nL 132.82359 80.970259 \nL 132.915291 144.105275 \nL 133.006992 138.092416 \nL 133.098692 159.137421 \nL 133.190393 149.366526 \nL 133.373795 99.760442 \nL 133.557197 141.850453 \nL 133.648898 137.340809 \nL 133.8323 153.124563 \nL 134.107402 120.805448 \nL 134.199103 147.111704 \nL 134.290804 141.850453 \nL 134.382505 138.844024 \nL 134.565907 124.563484 \nL 134.749309 133.582772 \nL 134.84101 118.550626 \nL 134.932711 141.098845 \nL 135.024411 111.78616 \nL 135.116112 132.079558 \nL 135.207813 115.544196 \nL 135.299514 117.047411 \nL 135.391215 138.092416 \nL 135.482916 115.544196 \nL 135.574617 144.856882 \nL 135.666318 131.32795 \nL 135.84972 149.366526 \nL 136.033121 120.805448 \nL 136.124822 165.901887 \nL 136.399925 104.270086 \nL 136.675028 189.953322 \nL 136.766729 188.450107 \nL 136.85843 171.914746 \nL 136.95013 173.417961 \nL 137.225233 140.347238 \nL 137.316934 177.927605 \nL 137.408635 167.405102 \nL 137.500336 178.679212 \nL 137.867139 144.105275 \nL 137.95884 149.366526 \nL 138.050541 143.353667 \nL 138.142242 123.811877 \nL 138.325644 144.856882 \nL 138.509046 154.627777 \nL 138.600747 141.098845 \nL 138.692448 168.156709 \nL 138.784149 159.889029 \nL 138.875849 132.831165 \nL 139.059251 149.366526 \nL 139.150952 147.111704 \nL 139.334354 121.557055 \nL 139.517756 160.640636 \nL 139.609457 131.32795 \nL 139.701158 144.856882 \nL 139.792858 138.844024 \nL 139.884559 185.443678 \nL 139.97626 177.175997 \nL 140.067961 153.124563 \nL 140.159662 193.711358 \nL 140.251363 182.437249 \nL 140.434765 131.32795 \nL 140.526466 179.430819 \nL 140.618167 174.921175 \nL 140.709867 139.595631 \nL 140.893269 198.221002 \nL 141.076671 152.372955 \nL 141.168372 150.118133 \nL 141.260073 138.844024 \nL 141.443475 160.640636 \nL 141.810278 144.105275 \nL 141.901979 156.130992 \nL 142.085381 196.717788 \nL 142.177082 185.443678 \nL 142.268783 204.985468 \nL 142.360484 198.97261 \nL 142.452185 159.137421 \nL 142.543886 160.640636 \nL 142.727287 147.863311 \nL 142.818988 148.614919 \nL 142.910689 154.627777 \nL 143.094091 214.004756 \nL 143.185792 207.991898 \nL 143.277493 156.130992 \nL 143.369194 160.640636 \nL 143.460895 154.627777 \nL 143.552596 180.182427 \nL 143.644296 175.672783 \nL 143.827698 163.647065 \nL 143.919399 153.87617 \nL 144.0111 158.385814 \nL 144.194502 180.182427 \nL 144.377904 141.850453 \nL 144.469605 162.143851 \nL 144.653006 135.085987 \nL 144.744707 128.321521 \nL 144.836408 138.092416 \nL 144.928109 131.32795 \nL 145.01981 132.079558 \nL 145.111511 147.863311 \nL 145.294913 126.818306 \nL 145.386614 127.569914 \nL 145.570015 167.405102 \nL 145.661716 149.366526 \nL 145.753417 150.869741 \nL 145.845118 150.869741 \nL 145.936819 154.627777 \nL 146.02852 169.659924 \nL 146.211922 150.869741 \nL 146.303623 156.882599 \nL 146.487024 147.111704 \nL 146.670426 163.647065 \nL 146.762127 144.856882 \nL 146.853828 164.398673 \nL 146.945529 147.111704 \nL 147.128931 167.405102 \nL 147.220632 155.379385 \nL 147.312333 175.672783 \nL 147.495734 129.824736 \nL 147.587435 145.608489 \nL 147.679136 129.824736 \nL 147.770837 162.143851 \nL 147.862538 154.627777 \nL 147.954239 180.182427 \nL 148.137641 143.353667 \nL 148.229342 144.105275 \nL 148.321043 135.837594 \nL 148.412743 141.850453 \nL 148.504444 177.927605 \nL 148.596145 154.627777 \nL 148.779547 173.417961 \nL 148.962949 126.818306 \nL 149.146351 147.863311 \nL 149.238052 129.824736 \nL 149.421453 168.156709 \nL 149.513154 165.15028 \nL 149.604855 146.360097 \nL 149.696556 168.908317 \nL 149.788257 158.385814 \nL 149.879958 134.33438 \nL 150.06336 173.417961 \nL 150.155061 164.398673 \nL 150.246761 183.188856 \nL 150.430163 92.244369 \nL 150.613565 137.340809 \nL 150.796967 156.882599 \nL 150.888668 94.499191 \nL 150.980369 105.021694 \nL 151.163771 153.87617 \nL 151.347172 85.479903 \nL 151.530574 149.366526 \nL 151.713976 178.679212 \nL 151.989079 141.850453 \nL 152.08078 140.347238 \nL 152.17248 165.901887 \nL 152.264181 141.098845 \nL 152.355882 77.96383 \nL 152.539284 146.360097 \nL 152.630985 142.60206 \nL 152.722686 113.289374 \nL 152.906088 139.595631 \nL 152.997789 150.869741 \nL 153.18119 89.989547 \nL 153.272891 127.569914 \nL 153.364592 123.06027 \nL 153.547994 145.608489 \nL 153.639695 140.347238 \nL 153.823097 97.50562 \nL 153.914798 71.950971 \nL 154.098199 123.06027 \nL 154.1899 124.563484 \nL 154.281601 131.32795 \nL 154.373302 126.066699 \nL 154.465003 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242.314469 152.372955 \nL 242.40617 194.462966 \nL 242.681273 177.175997 \nL 242.772973 171.163139 \nL 242.956375 183.940463 \nL 243.139777 146.360097 \nL 243.231478 155.379385 \nL 243.41488 193.711358 \nL 243.598282 147.863311 \nL 243.689983 174.169568 \nL 243.965085 144.105275 \nL 244.056786 167.405102 \nL 244.148487 162.143851 \nL 244.240188 166.653495 \nL 244.331889 164.398673 \nL 244.42359 203.482254 \nL 244.973795 148.614919 \nL 245.065496 149.366526 \nL 245.248898 142.60206 \nL 245.340599 154.627777 \nL 245.4323 151.621348 \nL 245.524001 153.87617 \nL 245.615701 147.111704 \nL 245.707402 174.921175 \nL 245.799103 147.863311 \nL 245.890804 149.366526 \nL 245.982505 177.927605 \nL 246.165907 158.385814 \nL 246.257608 162.143851 \nL 246.44101 126.066699 \nL 246.532711 140.347238 \nL 246.716112 183.188856 \nL 246.807813 182.437249 \nL 246.899514 154.627777 \nL 246.991215 176.42439 \nL 247.082916 144.105275 \nL 247.174617 146.360097 \nL 247.358019 135.085987 \nL 247.44972 150.118133 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115.544196 \nL 252.218167 140.347238 \nL 252.309867 138.844024 \nL 252.401568 129.824736 \nL 252.493269 136.589202 \nL 252.58497 132.831165 \nL 252.676671 145.608489 \nL 252.951774 113.289374 \nL 253.043475 141.098845 \nL 253.135176 116.295804 \nL 253.226877 141.850453 \nL 253.318577 129.073128 \nL 253.410278 140.347238 \nL 253.685381 41.886678 \nL 253.868783 142.60206 \nL 254.052185 123.811877 \nL 254.143886 132.079558 \nL 254.327287 104.270086 \nL 254.510689 138.844024 \nL 254.694091 117.047411 \nL 254.877493 143.353667 \nL 255.244296 33.618998 \nL 255.427698 134.33438 \nL 255.519399 149.366526 \nL 255.6111 114.792589 \nL 255.794502 140.347238 \nL 255.977904 128.321521 \nL 256.069605 139.595631 \nL 256.161305 110.282945 \nL 256.253006 112.537767 \nL 256.528109 153.124563 \nL 256.61981 144.105275 \nL 256.711511 119.302233 \nL 256.894913 132.079558 \nL 256.986614 129.824736 \nL 257.261716 100.51205 \nL 257.353417 110.282945 \nL 257.62852 81.721867 \nL 257.720221 60.676861 \nL 257.903623 120.805448 \nL 257.995324 132.831165 \nL 258.087024 118.550626 \nL 258.178725 119.302233 \nL 258.270426 130.576343 \nL 258.362127 129.073128 \nL 258.453828 130.576343 \nL 258.63723 119.302233 \nL 258.728931 92.995976 \nL 258.820632 108.028123 \nL 258.912333 107.276516 \nL 259.004033 114.792589 \nL 259.095734 89.23794 \nL 259.370837 113.289374 \nL 259.462538 102.015264 \nL 259.554239 112.537767 \nL 259.829342 74.205793 \nL 259.921043 90.741155 \nL 260.196145 77.212223 \nL 260.287846 46.396322 \nL 260.471248 57.670432 \nL 260.65465 98.257228 \nL 260.746351 89.989547 \nL 260.929752 97.50562 \nL 261.113154 109.531338 \nL 261.204855 97.50562 \nL 261.388257 127.569914 \nL 261.479958 120.05384 \nL 261.846761 38.880249 \nL 262.030163 108.77973 \nL 262.121864 102.015264 \nL 262.213565 105.773301 \nL 262.305266 101.263657 \nL 262.488668 114.040982 \nL 262.580369 145.608489 \nL 262.763771 101.263657 \nL 262.855471 123.811877 \nL 263.130574 90.741155 \nL 263.405677 126.066699 \nL 263.589079 92.995976 \nL 263.77248 113.289374 \nL 264.047583 92.995976 \nL 264.139284 92.995976 \nL 264.230985 114.792589 \nL 264.414387 76.460615 \nL 264.68949 121.557055 \nL 264.78119 97.50562 \nL 265.056293 119.302233 \nL 265.239695 88.486333 \nL 265.331396 89.23794 \nL 265.423097 92.995976 \nL 265.514798 105.773301 \nL 265.606499 139.595631 \nL 265.698199 120.05384 \nL 265.881601 126.066699 \nL 266.156704 96.754013 \nL 266.248405 99.760442 \nL 266.431807 111.78616 \nL 266.615208 97.50562 \nL 266.79861 110.282945 \nL 266.982012 89.23794 \nL 267.073713 98.257228 \nL 267.348816 77.96383 \nL 267.440517 93.747584 \nL 267.532218 90.741155 \nL 267.623918 105.021694 \nL 267.715619 91.492762 \nL 267.80732 112.537767 \nL 267.899021 95.250798 \nL 267.990722 125.315092 \nL 268.082423 104.270086 \nL 268.265825 165.15028 \nL 268.357526 155.379385 \nL 268.540927 96.754013 \nL 268.632628 100.51205 \nL 268.724329 95.250798 \nL 268.907731 152.372955 \nL 268.999432 150.118133 \nL 269.091133 119.302233 \nL 269.182834 135.837594 \nL 269.274535 124.563484 \nL 269.366236 131.32795 \nL 269.457937 117.047411 \nL 269.549637 121.557055 \nL 269.641338 114.792589 \nL 269.733039 95.250798 \nL 269.82474 124.563484 \nL 269.916441 111.78616 \nL 270.008142 82.473474 \nL 270.191544 111.78616 \nL 270.283245 100.51205 \nL 270.374946 105.773301 \nL 270.558347 98.257228 \nL 270.650048 91.492762 \nL 270.83345 120.05384 \nL 270.925151 112.537767 \nL 271.108553 132.079558 \nL 271.200254 124.563484 \nL 271.291955 163.647065 \nL 271.475356 116.295804 \nL 271.567057 113.289374 \nL 271.658758 126.818306 \nL 271.750459 115.544196 \nL 272.117263 153.124563 \nL 272.300665 137.340809 \nL 272.392365 153.87617 \nL 272.484066 149.366526 \nL 272.575767 120.05384 \nL 272.942571 167.405102 \nL 273.401075 120.05384 \nL 273.492776 138.092416 \nL 273.584477 131.32795 \nL 273.676178 149.366526 \nL 273.85958 141.850453 \nL 274.042982 177.175997 \nL 274.134683 165.901887 \nL 274.226384 123.811877 \nL 274.501486 193.711358 \nL 274.593187 186.946892 \nL 274.684888 163.647065 \nL 274.776589 165.15028 \nL 275.051692 155.379385 \nL 275.143393 135.085987 \nL 275.326794 164.398673 \nL 275.510196 139.595631 \nL 275.601897 164.398673 \nL 275.693598 144.105275 \nL 275.785299 144.856882 \nL 275.968701 171.163139 \nL 276.060402 177.927605 \nL 276.152102 177.175997 \nL 276.427205 117.047411 \nL 276.518906 129.073128 \nL 276.610607 163.647065 \nL 276.702308 157.634207 \nL 276.794009 121.557055 \nL 276.88571 161.392243 \nL 276.977411 158.385814 \nL 277.069112 139.595631 \nL 277.160812 174.921175 \nL 277.619317 143.353667 \nL 277.711018 172.666353 \nL 277.986121 150.869741 \nL 278.077821 153.124563 \nL 278.169522 150.869741 \nL 278.352924 141.850453 \nL 278.444625 161.392243 \nL 278.719728 141.098845 \nL 278.811429 153.87617 \nL 278.994831 139.595631 \nL 279.086531 176.42439 \nL 279.269933 162.895458 \nL 279.361634 163.647065 \nL 279.545036 146.360097 \nL 279.636737 185.443678 \nL 279.728438 178.679212 \nL 280.00354 123.811877 \nL 280.095241 121.557055 \nL 280.186942 139.595631 \nL 280.278643 138.844024 \nL 280.370344 141.850453 \nL 280.462045 126.818306 \nL 280.553746 155.379385 \nL 280.645447 150.118133 \nL 280.828849 171.163139 \nL 281.01225 135.085987 \nL 281.103951 164.398673 \nL 281.287353 141.850453 \nL 281.379054 147.111704 \nL 281.562456 100.51205 \nL 281.837559 173.417961 \nL 281.929259 144.105275 \nL 282.02096 148.614919 \nL 282.112661 174.921175 \nL 282.296063 100.51205 \nL 282.571166 163.647065 \nL 282.662867 179.430819 \nL 282.754568 175.672783 \nL 282.846268 163.647065 \nL 282.937969 134.33438 \nL 283.02967 138.844024 \nL 283.213072 141.098845 \nL 283.304773 173.417961 \nL 283.488175 89.989547 \nL 283.671577 153.124563 \nL 283.763278 131.32795 \nL 283.854978 133.582772 \nL 283.946679 148.614919 \nL 284.03838 133.582772 \nL 284.130081 149.366526 \nL 284.221782 121.557055 \nL 284.313483 147.111704 \nL 284.496885 104.270086 \nL 284.771987 169.659924 \nL 284.863688 119.302233 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295.592694 93.747584 \nL 295.684395 106.524908 \nL 295.776096 92.244369 \nL 295.867797 96.754013 \nL 296.051199 115.544196 \nL 296.2346 75.709008 \nL 296.418002 99.760442 \nL 296.509703 95.250798 \nL 296.601404 100.51205 \nL 296.876507 68.944542 \nL 296.968208 68.944542 \nL 297.059909 68.192935 \nL 297.151609 60.676861 \nL 297.335011 102.015264 \nL 297.426712 93.747584 \nL 297.610114 117.047411 \nL 297.793516 81.721867 \nL 297.885217 115.544196 \nL 298.25202 49.402751 \nL 298.435422 67.441327 \nL 298.527123 62.180076 \nL 298.618824 77.212223 \nL 298.710525 72.702579 \nL 298.893927 53.912395 \nL 299.077328 80.970259 \nL 299.169029 81.721867 \nL 299.26073 118.550626 \nL 299.352431 101.263657 \nL 299.444132 102.015264 \nL 299.535833 103.518479 \nL 299.627534 124.563484 \nL 299.719235 120.805448 \nL 299.994337 84.728296 \nL 300.177739 90.741155 \nL 300.452842 144.105275 \nL 300.544543 143.353667 \nL 300.636244 126.066699 \nL 300.819646 141.850453 \nL 301.094748 101.263657 \nL 301.27815 108.028123 \nL 301.369851 70.447757 \nL 301.461552 120.05384 \nL 301.553253 108.028123 \nL 301.644954 125.315092 \nL 301.736655 110.282945 \nL 301.828356 113.289374 \nL 301.920056 99.760442 \nL 302.011757 110.282945 \nL 302.103458 109.531338 \nL 302.195159 117.799018 \nL 302.28686 150.869741 \nL 302.378561 129.073128 \nL 302.470262 132.831165 \nL 302.561963 124.563484 \nL 302.653664 150.118133 \nL 302.745365 147.111704 \nL 302.928766 138.092416 \nL 303.020467 141.098845 \nL 303.112168 152.372955 \nL 303.387271 109.531338 \nL 303.478972 96.002406 \nL 303.662374 115.544196 \nL 303.845775 105.021694 \nL 303.937476 126.066699 \nL 304.029177 106.524908 \nL 304.212579 137.340809 \nL 304.30428 133.582772 \nL 304.395981 135.837594 \nL 304.487682 143.353667 \nL 304.671084 111.78616 \nL 305.221289 153.87617 \nL 305.31299 126.818306 \nL 305.404691 127.569914 \nL 305.588093 175.672783 \nL 305.679794 132.079558 \nL 305.863195 145.608489 \nL 305.954896 134.33438 \nL 306.046597 147.111704 \nL 306.413401 115.544196 \nL 306.596803 197.469395 \nL 306.688503 204.233861 \nL 306.780204 198.97261 \nL 306.963606 147.863311 \nL 307.055307 156.130992 \nL 307.238709 137.340809 \nL 307.422111 160.640636 \nL 307.605513 148.614919 \nL 307.697213 168.156709 \nL 307.880615 138.092416 \nL 307.972316 141.850453 \nL 308.064017 130.576343 \nL 308.614222 179.430819 \nL 308.705923 174.921175 \nL 308.797624 180.934034 \nL 309.072727 210.998327 \nL 309.164428 196.717788 \nL 309.256129 154.627777 \nL 309.34783 169.659924 \nL 309.439531 161.392243 \nL 309.531231 141.850453 \nL 309.714633 174.921175 \nL 309.806334 162.143851 \nL 309.898035 168.156709 \nL 309.989736 162.143851 \nL 310.081437 141.850453 \nL 310.173138 154.627777 \nL 310.264839 150.869741 \nL 310.35654 161.392243 \nL 310.448241 158.385814 \nL 310.631642 201.227432 \nL 310.723343 195.214573 \nL 310.906745 171.163139 \nL 310.998446 171.163139 \nL 311.090147 160.640636 \nL 311.273549 202.730646 \nL 311.36525 191.456536 \nL 311.548651 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180.182427 \nL 214.070591 162.143851 \nL 214.162291 108.028123 \nL 214.253992 119.302233 \nL 214.437394 184.692071 \nL 214.620796 135.837594 \nL 214.804198 180.934034 \nL 214.895899 153.124563 \nL 214.9876 182.437249 \nL 215.079301 141.098845 \nL 215.262702 177.175997 \nL 215.446104 147.111704 \nL 215.537805 187.6985 \nL 215.904609 102.015264 \nL 216.08801 171.914746 \nL 216.271412 184.692071 \nL 216.546515 150.869741 \nL 216.638216 128.321521 \nL 216.729917 156.882599 \nL 216.821618 145.608489 \nL 217.09672 167.405102 \nL 217.188421 150.118133 \nL 217.280122 168.908317 \nL 217.371823 115.544196 \nL 217.555225 179.430819 \nL 217.646926 171.163139 \nL 217.738627 102.766872 \nL 217.922029 150.118133 \nL 218.013729 144.105275 \nL 218.10543 171.914746 \nL 218.288832 116.295804 \nL 218.472234 153.124563 \nL 218.563935 141.098845 \nL 218.747337 171.163139 \nL 218.839038 141.098845 \nL 218.930738 155.379385 \nL 219.205841 135.085987 \nL 219.297542 154.627777 \nL 219.389243 138.092416 \nL 219.480944 101.263657 \nL 219.572645 110.282945 \nL 219.756047 147.111704 \nL 219.847748 115.544196 \nL 219.939448 162.143851 \nL 220.031149 135.085987 \nL 220.12285 162.895458 \nL 220.489654 81.721867 \nL 220.581355 94.499191 \nL 220.764757 135.837594 \nL 220.856457 106.524908 \nL 221.039859 147.111704 \nL 221.223261 105.773301 \nL 221.314962 79.467045 \nL 221.498364 134.33438 \nL 221.681766 149.366526 \nL 221.865167 120.05384 \nL 221.956868 137.340809 \nL 222.14027 94.499191 \nL 222.231971 96.002406 \nL 222.323672 123.811877 \nL 222.415373 120.805448 \nL 222.507074 123.06027 \nL 222.690476 93.747584 \nL 222.782176 98.257228 \nL 222.873877 137.340809 \nL 222.965578 135.837594 \nL 223.14898 125.315092 \nL 223.240681 117.047411 \nL 223.424083 135.085987 \nL 223.607485 117.047411 \nL 223.699185 123.06027 \nL 223.790886 120.05384 \nL 223.882587 74.205793 \nL 223.974288 100.51205 \nL 224.065989 99.760442 \nL 224.15769 110.282945 \nL 224.249391 96.002406 \nL 224.432793 117.047411 \nL 224.524494 111.78616 \nL 224.707895 133.582772 \nL 224.799596 97.50562 \nL 224.891297 99.760442 \nL 225.074699 117.047411 \nL 225.258101 92.244369 \nL 225.349802 96.002406 \nL 225.441503 81.721867 \nL 225.533204 92.244369 \nL 225.624904 76.460615 \nL 225.808306 132.831165 \nL 225.900007 129.073128 \nL 225.991708 103.518479 \nL 226.083409 123.811877 \nL 226.17511 118.550626 \nL 226.266811 92.995976 \nL 226.358512 98.257228 \nL 226.633614 146.360097 \nL 226.908717 119.302233 \nL 227.000418 119.302233 \nL 227.092119 128.321521 \nL 227.18382 111.034552 \nL 227.275521 114.792589 \nL 227.367222 127.569914 \nL 227.458923 99.008835 \nL 227.550623 121.557055 \nL 227.642324 87.734725 \nL 227.825726 135.085987 \nL 227.917427 97.50562 \nL 228.009128 134.33438 \nL 228.284231 107.276516 \nL 228.375932 109.531338 \nL 228.467632 78.715437 \nL 228.559333 84.728296 \nL 228.651034 117.047411 \nL 228.742735 94.499191 \nL 228.834436 102.766872 \nL 228.926137 92.995976 \nL 229.109539 45.644715 \nL 229.292941 95.250798 \nL 229.384642 88.486333 \nL 229.568043 118.550626 \nL 229.659744 109.531338 \nL 229.843146 53.160788 \nL 230.026548 112.537767 \nL 230.118249 105.773301 \nL 230.20995 108.028123 \nL 230.301651 96.754013 \nL 230.393351 66.68972 \nL 230.576753 106.524908 \nL 230.851856 61.428469 \nL 231.035258 65.186505 \nL 231.126959 49.402751 \nL 231.21866 60.676861 \nL 231.31036 48.651144 \nL 231.402061 59.925254 \nL 231.493762 102.015264 \nL 231.677164 53.160788 \nL 231.860566 108.77973 \nL 231.952267 105.773301 \nL 232.043968 56.167217 \nL 232.22737 100.51205 \nL 232.31907 116.295804 \nL 232.410771 115.544196 \nL 232.502472 120.805448 \nL 232.685874 82.473474 \nL 232.777575 98.257228 \nL 232.869276 89.23794 \nL 232.960977 92.244369 \nL 233.144379 119.302233 \nL 233.236079 139.595631 \nL 233.419481 120.05384 \nL 233.602883 139.595631 \nL 233.694584 110.282945 \nL 233.786285 114.040982 \nL 233.877986 120.805448 \nL 233.969687 118.550626 \nL 234.061388 156.130992 \nL 234.153089 131.32795 \nL 234.244789 134.33438 \nL 234.428191 164.398673 \nL 234.519892 171.914746 \nL 234.794995 98.257228 \nL 234.886696 131.32795 \nL 234.978397 126.818306 \nL 235.070098 128.321521 \nL 235.253499 168.156709 \nL 235.3452 164.398673 \nL 235.528602 148.614919 \nL 235.620303 154.627777 \nL 235.895406 90.741155 \nL 236.078807 135.837594 \nL 236.262209 117.047411 \nL 236.35391 149.366526 \nL 236.720714 113.289374 \nL 236.812415 111.78616 \nL 236.904116 113.289374 \nL 236.995817 134.33438 \nL 237.087517 117.047411 \nL 237.179218 127.569914 \nL 237.270919 117.047411 \nL 237.36262 130.576343 \nL 237.454321 113.289374 \nL 237.546022 117.799018 \nL 237.637723 163.647065 \nL 237.821125 105.773301 \nL 238.096227 180.182427 \nL 238.187928 177.927605 \nL 238.37133 152.372955 \nL 238.554732 168.156709 \nL 238.646433 156.130992 \nL 238.738134 115.544196 \nL 238.829835 125.315092 \nL 238.921536 165.901887 \nL 239.104937 123.811877 \nL 239.288339 158.385814 \nL 239.471741 132.079558 \nL 239.563442 133.582772 \nL 239.655143 174.921175 \nL 239.746844 157.634207 \nL 239.838545 172.666353 \nL 240.021946 142.60206 \nL 240.113647 162.143851 \nL 240.205348 152.372955 \nL 240.297049 156.130992 \nL 240.38875 179.430819 \nL 240.572152 160.640636 \nL 240.755554 143.353667 \nL 240.938955 192.208144 \nL 241.030656 203.482254 \nL 241.122357 195.96618 \nL 241.305759 127.569914 \nL 241.489161 165.15028 \nL 241.580862 154.627777 \nL 241.672563 155.379385 \nL 241.764264 189.953322 \nL 241.855964 185.443678 \nL 241.947665 169.659924 \nL 242.039366 184.692071 \nL 242.314469 141.098845 \nL 242.40617 143.353667 \nL 242.497871 160.640636 \nL 242.589572 153.87617 \nL 242.681273 154.627777 \nL 242.864674 148.614919 \nL 242.956375 152.372955 \nL 243.048076 196.717788 \nL 243.231478 170.411531 \nL 243.41488 151.621348 \nL 243.506581 165.901887 \nL 243.598282 155.379385 \nL 243.689983 183.940463 \nL 243.873384 158.385814 \nL 244.056786 195.96618 \nL 244.240188 165.15028 \nL 244.331889 214.756364 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112.537767 \nL 249.742242 152.372955 \nL 249.833943 150.869741 \nL 249.925644 117.799018 \nL 250.200747 188.450107 \nL 250.384149 99.008835 \nL 250.56755 142.60206 \nL 250.659251 144.856882 \nL 250.750952 110.282945 \nL 250.842653 156.882599 \nL 250.934354 143.353667 \nL 251.117756 162.895458 \nL 251.209457 163.647065 \nL 251.301158 171.163139 \nL 251.392858 169.659924 \nL 251.851363 92.995976 \nL 252.034765 126.066699 \nL 252.218167 139.595631 \nL 252.309867 123.06027 \nL 252.401568 147.863311 \nL 252.493269 137.340809 \nL 252.58497 158.385814 \nL 252.768372 120.05384 \nL 252.860073 117.799018 \nL 252.951774 126.818306 \nL 253.043475 109.531338 \nL 253.226877 147.111704 \nL 253.318577 145.608489 \nL 253.410278 141.098845 \nL 253.501979 126.066699 \nL 253.59368 135.085987 \nL 253.685381 120.05384 \nL 253.960484 158.385814 \nL 254.143886 103.518479 \nL 254.327287 156.882599 \nL 254.510689 133.582772 \nL 254.60239 133.582772 \nL 254.785792 115.544196 \nL 254.969194 171.914746 \nL 255.060895 141.098845 \nL 255.152596 159.889029 \nL 255.244296 133.582772 \nL 255.335997 139.595631 \nL 255.427698 92.995976 \nL 255.519399 102.015264 \nL 255.6111 105.773301 \nL 255.702801 95.250798 \nL 255.886203 108.028123 \nL 256.161305 82.473474 \nL 256.344707 129.073128 \nL 256.528109 115.544196 \nL 256.61981 124.563484 \nL 256.711511 99.760442 \nL 256.894913 123.811877 \nL 256.986614 111.034552 \nL 257.078314 132.831165 \nL 257.170015 124.563484 \nL 257.261716 90.741155 \nL 257.353417 102.015264 \nL 257.445118 130.576343 \nL 257.62852 102.015264 \nL 257.720221 103.518479 \nL 257.811922 102.015264 \nL 257.903623 114.792589 \nL 257.995324 61.428469 \nL 258.087024 79.467045 \nL 258.178725 123.06027 \nL 258.270426 89.23794 \nL 258.362127 111.034552 \nL 258.453828 83.225081 \nL 258.728931 131.32795 \nL 258.912333 61.428469 \nL 259.004033 79.467045 \nL 259.095734 68.192935 \nL 259.462538 132.079558 \nL 259.554239 92.244369 \nL 259.64594 93.747584 \nL 259.737641 117.047411 \nL 259.829342 114.040982 \nL 259.921043 100.51205 \nL 260.012743 120.805448 \nL 260.287846 74.957401 \nL 260.379547 79.467045 \nL 260.471248 77.96383 \nL 260.562949 129.073128 \nL 260.65465 125.315092 \nL 260.746351 123.06027 \nL 260.838052 103.518479 \nL 261.113154 135.837594 \nL 261.296556 73.454186 \nL 261.479958 130.576343 \nL 261.571659 135.085987 \nL 261.66336 104.270086 \nL 261.846761 123.811877 \nL 261.938462 104.270086 \nL 262.030163 131.32795 \nL 262.213565 97.50562 \nL 262.305266 108.028123 \nL 262.488668 79.467045 \nL 262.580369 102.015264 \nL 262.67207 95.250798 \nL 262.763771 98.257228 \nL 262.855471 96.002406 \nL 262.947172 89.989547 \nL 263.038873 112.537767 \nL 263.130574 111.034552 \nL 263.405677 89.989547 \nL 263.497378 107.276516 \nL 263.68078 72.702579 \nL 263.77248 74.205793 \nL 263.864181 105.773301 \nL 263.955882 90.741155 \nL 264.230985 126.818306 \nL 264.322686 101.263657 \nL 264.414387 130.576343 \nL 264.506088 113.289374 \nL 264.597789 120.05384 \nL 264.68949 148.614919 \nL 264.964592 105.773301 \nL 265.056293 68.192935 \nL 265.239695 111.034552 \nL 265.331396 135.837594 \nL 265.423097 111.034552 \nL 265.514798 129.073128 \nL 265.606499 97.50562 \nL 265.698199 131.32795 \nL 265.881601 108.028123 \nL 265.973302 132.831165 \nL 266.065003 108.028123 \nL 266.156704 111.034552 \nL 266.248405 101.263657 \nL 266.431807 123.811877 \nL 266.706909 80.970259 \nL 266.79861 144.105275 \nL 266.890311 138.092416 \nL 266.982012 159.137421 \nL 267.073713 149.366526 \nL 267.257115 99.760442 \nL 267.440517 141.850453 \nL 267.532218 137.340809 \nL 267.715619 153.124563 \nL 267.990722 120.805448 \nL 268.082423 147.111704 \nL 268.174124 141.850453 \nL 268.265825 138.844024 \nL 268.449227 124.563484 \nL 268.632628 133.582772 \nL 268.724329 118.550626 \nL 268.81603 141.098845 \nL 268.907731 111.78616 \nL 268.999432 132.079558 \nL 269.091133 115.544196 \nL 269.182834 117.047411 \nL 269.274535 138.092416 \nL 269.366236 115.544196 \nL 269.457937 144.856882 \nL 269.549637 131.32795 \nL 269.733039 149.366526 \nL 269.916441 120.805448 \nL 270.008142 165.901887 \nL 270.283245 104.270086 \nL 270.558347 189.953322 \nL 270.650048 188.450107 \nL 270.741749 171.914746 \nL 270.83345 173.417961 \nL 271.108553 140.347238 \nL 271.200254 177.927605 \nL 271.291955 167.405102 \nL 271.383655 178.679212 \nL 271.750459 144.105275 \nL 271.84216 149.366526 \nL 271.933861 143.353667 \nL 272.025562 123.811877 \nL 272.208964 144.856882 \nL 272.392365 154.627777 \nL 272.484066 141.098845 \nL 272.575767 168.156709 \nL 272.667468 159.889029 \nL 272.759169 132.831165 \nL 272.942571 149.366526 \nL 273.034272 147.111704 \nL 273.217674 121.557055 \nL 273.401075 160.640636 \nL 273.492776 131.32795 \nL 273.584477 144.856882 \nL 273.676178 138.844024 \nL 273.767879 185.443678 \nL 273.85958 177.175997 \nL 273.951281 153.124563 \nL 274.042982 193.711358 \nL 274.134683 182.437249 \nL 274.318084 131.32795 \nL 274.409785 179.430819 \nL 274.501486 174.921175 \nL 274.593187 139.595631 \nL 274.776589 198.221002 \nL 274.959991 152.372955 \nL 275.051692 150.118133 \nL 275.143393 138.844024 \nL 275.326794 160.640636 \nL 275.693598 144.105275 \nL 275.785299 156.130992 \nL 275.968701 196.717788 \nL 276.060402 185.443678 \nL 276.152102 204.985468 \nL 276.243803 198.97261 \nL 276.335504 159.137421 \nL 276.427205 160.640636 \nL 276.610607 147.863311 \nL 276.702308 148.614919 \nL 276.794009 154.627777 \nL 276.977411 214.004756 \nL 277.069112 207.991898 \nL 277.160812 156.130992 \nL 277.252513 160.640636 \nL 277.344214 154.627777 \nL 277.435915 180.182427 \nL 277.527616 175.672783 \nL 277.711018 163.647065 \nL 277.802719 153.87617 \nL 277.89442 158.385814 \nL 278.077821 180.182427 \nL 278.261223 141.850453 \nL 278.352924 162.143851 \nL 278.536326 135.085987 \nL 278.628027 128.321521 \nL 278.719728 138.092416 \nL 278.811429 131.32795 \nL 278.90313 132.079558 \nL 278.994831 147.863311 \nL 279.178232 126.818306 \nL 279.269933 127.569914 \nL 279.453335 167.405102 \nL 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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "train.plot()\n",
    "val.plot()\n",
    "pred_val.plot()\n",
    "print(\"MAPE:\", mape(pred_val, val))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Improvement 2: Filtering out low-amplitude waves\n",
    "The decomposition of the DFT into the frequency domain allows us to selectively filter out waves with low amplitudes. This allows us to keep strong seasonal trends while discarding some noise. This is achieved in the FFT model by passing the optional argument `nr_freqs_to_keep`. This argument represents the total number of frequencies that will be kept. For instance, if a value of 20 is passed, only the 20 frequencies with the highest amplitudes will be utilized. The default value is set to 10."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = FFT(nr_freqs_to_keep=20)\n",
    "model.fit(train)\n",
    "pred_val = model.predict(len(val))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We get a signal that is less noisy. Depending on the data set, this might be a better forecast. Looking at the error metric, we can see that this model performs significantly better than the previous models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "MAPE: 23.280281955513267\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
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122.308662 \nL 66.707238 125.315092 \nL 66.798939 130.576343 \nL 66.89064 150.869741 \nL 67.074042 121.557055 \nL 67.165743 117.799018 \nL 67.257443 138.844024 \nL 67.349144 102.015264 \nL 67.532546 121.557055 \nL 67.715948 93.747584 \nL 67.807649 68.192935 \nL 67.991051 144.856882 \nL 68.082752 138.844024 \nL 68.174453 159.137421 \nL 68.266153 150.118133 \nL 68.357854 156.130992 \nL 68.449555 146.360097 \nL 68.632957 90.741155 \nL 68.90806 162.895458 \nL 69.183162 133.582772 \nL 69.366564 167.405102 \nL 69.549966 111.034552 \nL 69.825069 138.844024 \nL 70.008471 173.417961 \nL 70.283573 133.582772 \nL 70.375274 130.576343 \nL 70.466975 146.360097 \nL 70.558676 186.946892 \nL 70.650377 180.182427 \nL 70.742078 165.15028 \nL 70.92548 100.51205 \nL 71.017181 157.634207 \nL 71.108881 151.621348 \nL 71.200582 169.659924 \nL 71.475685 131.32795 \nL 71.750788 109.531338 \nL 71.93419 128.321521 \nL 72.02589 162.143851 \nL 72.117591 161.392243 \nL 72.209292 147.111704 \nL 72.392694 195.96618 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78.07815 198.221002 \nL 78.169851 180.934034 \nL 78.353253 186.195285 \nL 78.536655 128.321521 \nL 78.628356 138.092416 \nL 78.720056 155.379385 \nL 78.903458 143.353667 \nL 78.995159 169.659924 \nL 79.178561 145.608489 \nL 79.270262 182.437249 \nL 79.545365 115.544196 \nL 79.728766 176.42439 \nL 79.820467 123.811877 \nL 79.912168 130.576343 \nL 80.09557 180.182427 \nL 80.187271 162.143851 \nL 80.278972 108.028123 \nL 80.370673 119.302233 \nL 80.554075 184.692071 \nL 80.737476 135.837594 \nL 80.920878 180.934034 \nL 81.012579 153.124563 \nL 81.10428 182.437249 \nL 81.195981 141.098845 \nL 81.379383 177.175997 \nL 81.562784 147.111704 \nL 81.654485 187.6985 \nL 82.021289 102.015264 \nL 82.204691 171.914746 \nL 82.388093 184.692071 \nL 82.663195 150.869741 \nL 82.754896 128.321521 \nL 82.846597 156.882599 \nL 82.938298 145.608489 \nL 83.213401 167.405102 \nL 83.305102 150.118133 \nL 83.396803 168.908317 \nL 83.488503 115.544196 \nL 83.671905 179.430819 \nL 83.763606 171.163139 \nL 83.855307 102.766872 \nL 84.038709 150.118133 \nL 84.13041 144.105275 \nL 84.222111 171.914746 \nL 84.405513 116.295804 \nL 84.588914 153.124563 \nL 84.680615 141.098845 \nL 84.864017 171.163139 \nL 84.955718 141.098845 \nL 85.047419 155.379385 \nL 85.322522 135.085987 \nL 85.414222 154.627777 \nL 85.505923 138.092416 \nL 85.597624 101.263657 \nL 85.689325 110.282945 \nL 85.872727 147.111704 \nL 85.964428 115.544196 \nL 86.056129 162.143851 \nL 86.14783 135.085987 \nL 86.239531 162.895458 \nL 86.606334 81.721867 \nL 86.698035 94.499191 \nL 86.881437 135.837594 \nL 86.973138 106.524908 \nL 87.15654 147.111704 \nL 87.339941 105.773301 \nL 87.431642 79.467045 \nL 87.615044 134.33438 \nL 87.798446 149.366526 \nL 87.981848 120.05384 \nL 88.073549 137.340809 \nL 88.25695 94.499191 \nL 88.348651 96.002406 \nL 88.440352 123.811877 \nL 88.532053 120.805448 \nL 88.623754 123.06027 \nL 88.807156 93.747584 \nL 88.898857 98.257228 \nL 88.990558 137.340809 \nL 89.082259 135.837594 \nL 89.26566 125.315092 \nL 89.357361 117.047411 \nL 89.540763 135.085987 \nL 89.724165 117.047411 \nL 89.815866 123.06027 \nL 89.907567 120.05384 \nL 89.999268 74.205793 \nL 90.090969 100.51205 \nL 90.182669 99.760442 \nL 90.27437 110.282945 \nL 90.366071 96.002406 \nL 90.549473 117.047411 \nL 90.641174 111.78616 \nL 90.824576 133.582772 \nL 90.916277 97.50562 \nL 91.007978 99.760442 \nL 91.191379 117.047411 \nL 91.374781 92.244369 \nL 91.466482 96.002406 \nL 91.558183 81.721867 \nL 91.649884 92.244369 \nL 91.741585 76.460615 \nL 91.924987 132.831165 \nL 92.016688 129.073128 \nL 92.108388 103.518479 \nL 92.200089 123.811877 \nL 92.29179 118.550626 \nL 92.383491 92.995976 \nL 92.475192 98.257228 \nL 92.750295 146.360097 \nL 93.025397 119.302233 \nL 93.117098 119.302233 \nL 93.208799 128.321521 \nL 93.3005 111.034552 \nL 93.392201 114.792589 \nL 93.483902 127.569914 \nL 93.575603 99.008835 \nL 93.667304 121.557055 \nL 93.759005 87.734725 \nL 93.942407 135.085987 \nL 94.034107 97.50562 \nL 94.125808 134.33438 \nL 94.400911 107.276516 \nL 94.492612 109.531338 \nL 94.584313 78.715437 \nL 94.676014 84.728296 \nL 94.767715 117.047411 \nL 94.859416 94.499191 \nL 94.951116 102.766872 \nL 95.042817 92.995976 \nL 95.226219 45.644715 \nL 95.409621 95.250798 \nL 95.501322 88.486333 \nL 95.684724 118.550626 \nL 95.776425 109.531338 \nL 95.959826 53.160788 \nL 96.143228 112.537767 \nL 96.234929 105.773301 \nL 96.32663 108.028123 \nL 96.418331 96.754013 \nL 96.510032 66.68972 \nL 96.693434 106.524908 \nL 96.968536 61.428469 \nL 97.151938 65.186505 \nL 97.243639 49.402751 \nL 97.33534 60.676861 \nL 97.427041 48.651144 \nL 97.518742 59.925254 \nL 97.610443 102.015264 \nL 97.793844 53.160788 \nL 97.977246 108.77973 \nL 98.068947 105.773301 \nL 98.160648 56.167217 \nL 98.34405 100.51205 \nL 98.435751 116.295804 \nL 98.527452 115.544196 \nL 98.619153 120.805448 \nL 98.802554 82.473474 \nL 98.894255 98.257228 \nL 98.985956 89.23794 \nL 99.077657 92.244369 \nL 99.261059 119.302233 \nL 99.35276 139.595631 \nL 99.536162 120.05384 \nL 99.719563 139.595631 \nL 99.811264 110.282945 \nL 99.902965 114.040982 \nL 99.994666 120.805448 \nL 100.086367 118.550626 \nL 100.178068 156.130992 \nL 100.269769 131.32795 \nL 100.36147 134.33438 \nL 100.544872 164.398673 \nL 100.636572 171.914746 \nL 100.911675 98.257228 \nL 101.003376 131.32795 \nL 101.095077 126.818306 \nL 101.186778 128.321521 \nL 101.37018 168.156709 \nL 101.461881 164.398673 \nL 101.645282 148.614919 \nL 101.736983 154.627777 \nL 102.012086 90.741155 \nL 102.195488 135.837594 \nL 102.37889 117.047411 \nL 102.470591 149.366526 \nL 102.837394 113.289374 \nL 102.929095 111.78616 \nL 103.020796 113.289374 \nL 103.112497 134.33438 \nL 103.204198 117.047411 \nL 103.295899 127.569914 \nL 103.3876 117.047411 \nL 103.479301 130.576343 \nL 103.571001 113.289374 \nL 103.662702 117.799018 \nL 103.754403 163.647065 \nL 103.937805 105.773301 \nL 104.212908 180.182427 \nL 104.304609 177.927605 \nL 104.48801 152.372955 \nL 104.671412 168.156709 \nL 104.763113 156.130992 \nL 104.854814 115.544196 \nL 104.946515 125.315092 \nL 105.038216 165.901887 \nL 105.221618 123.811877 \nL 105.405019 158.385814 \nL 105.588421 132.079558 \nL 105.680122 133.582772 \nL 105.771823 174.921175 \nL 105.863524 157.634207 \nL 105.955225 172.666353 \nL 106.138627 142.60206 \nL 106.230328 162.143851 \nL 106.322029 152.372955 \nL 106.413729 156.130992 \nL 106.50543 179.430819 \nL 106.688832 160.640636 \nL 106.872234 143.353667 \nL 107.055636 192.208144 \nL 107.147337 203.482254 \nL 107.239038 195.96618 \nL 107.422439 127.569914 \nL 107.605841 165.15028 \nL 107.697542 154.627777 \nL 107.789243 155.379385 \nL 107.880944 189.953322 \nL 107.972645 185.443678 \nL 108.064346 169.659924 \nL 108.156047 184.692071 \nL 108.431149 141.098845 \nL 108.52285 143.353667 \nL 108.614551 160.640636 \nL 108.706252 153.87617 \nL 108.797953 154.627777 \nL 108.981355 148.614919 \nL 109.073056 152.372955 \nL 109.164757 196.717788 \nL 109.348158 170.411531 \nL 109.53156 151.621348 \nL 109.623261 165.901887 \nL 109.714962 155.379385 \nL 109.806663 183.940463 \nL 109.990065 158.385814 \nL 110.173466 195.96618 \nL 110.356868 165.15028 \nL 110.448569 214.756364 \nL 110.54027 209.495112 \nL 110.723672 122.308662 \nL 110.815373 145.608489 \nL 110.907074 142.60206 \nL 110.998775 143.353667 \nL 111.090476 139.595631 \nL 111.182176 156.882599 \nL 111.273877 154.627777 \nL 111.457279 152.372955 \nL 111.54898 180.934034 \nL 111.915784 135.837594 \nL 112.007485 134.33438 \nL 112.099185 140.347238 \nL 112.282587 171.163139 \nL 112.55769 107.276516 \nL 112.832793 192.208144 \nL 112.924494 175.672783 \nL 113.107895 131.32795 \nL 113.199596 135.837594 \nL 113.291297 147.111704 \nL 113.382998 117.047411 \nL 113.474699 166.653495 \nL 113.5664 151.621348 \nL 113.658101 164.398673 \nL 113.841503 130.576343 \nL 113.933204 139.595631 \nL 114.024904 138.844024 \nL 114.208306 132.831165 \nL 114.300007 171.914746 \nL 114.483409 136.589202 \nL 114.666811 123.06027 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120.05384 \nL 120.077164 158.385814 \nL 120.260566 103.518479 \nL 120.443968 156.882599 \nL 120.62737 133.582772 \nL 120.71907 133.582772 \nL 120.902472 115.544196 \nL 121.085874 171.914746 \nL 121.177575 141.098845 \nL 121.269276 159.889029 \nL 121.360977 133.582772 \nL 121.452678 139.595631 \nL 121.544379 92.995976 \nL 121.636079 102.015264 \nL 121.72778 105.773301 \nL 121.819481 95.250798 \nL 122.002883 108.028123 \nL 122.277986 82.473474 \nL 122.461388 129.073128 \nL 122.644789 115.544196 \nL 122.73649 124.563484 \nL 122.828191 99.760442 \nL 123.011593 123.811877 \nL 123.103294 111.034552 \nL 123.194995 132.831165 \nL 123.286696 124.563484 \nL 123.378397 90.741155 \nL 123.470098 102.015264 \nL 123.561798 130.576343 \nL 123.7452 102.015264 \nL 123.836901 103.518479 \nL 123.928602 102.015264 \nL 124.020303 114.792589 \nL 124.112004 61.428469 \nL 124.203705 79.467045 \nL 124.295406 123.06027 \nL 124.387107 89.23794 \nL 124.478807 111.034552 \nL 124.570508 83.225081 \nL 124.845611 131.32795 \nL 125.029013 61.428469 \nL 125.120714 79.467045 \nL 125.212415 68.192935 \nL 125.579218 132.079558 \nL 125.670919 92.244369 \nL 125.76262 93.747584 \nL 125.854321 117.047411 \nL 125.946022 114.040982 \nL 126.037723 100.51205 \nL 126.129424 120.805448 \nL 126.404526 74.957401 \nL 126.496227 79.467045 \nL 126.587928 77.96383 \nL 126.679629 129.073128 \nL 126.77133 125.315092 \nL 126.863031 123.06027 \nL 126.954732 103.518479 \nL 127.229835 135.837594 \nL 127.413236 73.454186 \nL 127.596638 130.576343 \nL 127.688339 135.085987 \nL 127.78004 104.270086 \nL 127.963442 123.811877 \nL 128.055143 104.270086 \nL 128.146844 131.32795 \nL 128.330245 97.50562 \nL 128.421946 108.028123 \nL 128.605348 79.467045 \nL 128.697049 102.015264 \nL 128.78875 95.250798 \nL 128.880451 98.257228 \nL 128.972152 96.002406 \nL 129.063853 89.989547 \nL 129.155554 112.537767 \nL 129.247254 111.034552 \nL 129.522357 89.989547 \nL 129.614058 107.276516 \nL 129.79746 72.702579 \nL 129.889161 74.205793 \nL 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216.454814 162.895458 \nL 216.546515 135.085987 \nL 216.638216 150.118133 \nL 216.821618 120.805448 \nL 217.09672 173.417961 \nL 217.280122 132.079558 \nL 217.371823 92.995976 \nL 217.555225 149.366526 \nL 217.738627 123.06027 \nL 218.013729 173.417961 \nL 218.10543 147.111704 \nL 218.197131 166.653495 \nL 218.288832 160.640636 \nL 218.380533 117.799018 \nL 218.472234 124.563484 \nL 218.563935 159.889029 \nL 218.655636 141.850453 \nL 218.747337 151.621348 \nL 218.839038 104.270086 \nL 219.022439 155.379385 \nL 219.11414 163.647065 \nL 219.205841 120.05384 \nL 219.297542 175.672783 \nL 219.480944 149.366526 \nL 219.572645 157.634207 \nL 219.664346 147.111704 \nL 219.756047 160.640636 \nL 220.031149 110.282945 \nL 220.214551 136.589202 \nL 220.306252 146.360097 \nL 220.489654 56.918825 \nL 220.673056 150.118133 \nL 220.764757 145.608489 \nL 220.856457 120.805448 \nL 220.948158 141.850453 \nL 221.039859 120.805448 \nL 221.13156 137.340809 \nL 221.223261 124.563484 \nL 221.314962 132.079558 \nL 221.498364 102.015264 \nL 221.590065 99.760442 \nL 221.681766 137.340809 \nL 221.773466 134.33438 \nL 221.865167 135.837594 \nL 222.048569 153.87617 \nL 222.231971 118.550626 \nL 222.323672 146.360097 \nL 222.415373 105.021694 \nL 222.598775 130.576343 \nL 222.690476 120.05384 \nL 222.782176 158.385814 \nL 223.057279 75.709008 \nL 223.240681 116.295804 \nL 223.424083 62.931683 \nL 223.515784 128.321521 \nL 223.607485 121.557055 \nL 223.699185 132.831165 \nL 223.790886 119.302233 \nL 223.882587 123.06027 \nL 223.974288 121.557055 \nL 224.15769 150.869741 \nL 224.249391 104.270086 \nL 224.432793 137.340809 \nL 224.524494 132.079558 \nL 224.616195 138.092416 \nL 224.707895 120.05384 \nL 224.891297 141.850453 \nL 224.982998 114.040982 \nL 225.074699 135.837594 \nL 225.1664 104.270086 \nL 225.258101 105.021694 \nL 225.349802 108.028123 \nL 225.533204 126.818306 \nL 225.624904 85.479903 \nL 225.716605 122.308662 \nL 225.991708 97.50562 \nL 226.266811 88.486333 \nL 226.450213 150.869741 \nL 226.541913 115.544196 \nL 226.633614 117.047411 \nL 226.725315 121.557055 \nL 226.817016 117.047411 \nL 226.908717 89.989547 \nL 227.000418 124.563484 \nL 227.092119 121.557055 \nL 227.18382 102.015264 \nL 227.367222 127.569914 \nL 227.458923 123.06027 \nL 227.550623 111.78616 \nL 227.642324 130.576343 \nL 227.734025 121.557055 \nL 227.825726 128.321521 \nL 228.009128 96.754013 \nL 228.19253 128.321521 \nL 228.284231 132.079558 \nL 228.559333 90.741155 \nL 228.742735 119.302233 \nL 228.834436 119.302233 \nL 228.926137 127.569914 \nL 229.20124 91.492762 \nL 229.292941 125.315092 \nL 229.384642 101.263657 \nL 229.476342 135.085987 \nL 229.568043 112.537767 \nL 229.659744 123.811877 \nL 229.843146 88.486333 \nL 229.934847 89.989547 \nL 230.118249 100.51205 \nL 230.301651 56.918825 \nL 230.485052 135.837594 \nL 230.576753 143.353667 \nL 230.668454 124.563484 \nL 230.760155 136.589202 \nL 231.035258 102.015264 \nL 231.126959 108.77973 \nL 231.21866 121.557055 \nL 231.31036 114.040982 \nL 231.402061 120.805448 \nL 231.585463 82.473474 \nL 231.768865 140.347238 \nL 231.860566 138.092416 \nL 231.952267 129.824736 \nL 232.043968 143.353667 \nL 232.135669 126.066699 \nL 232.22737 128.321521 \nL 232.31907 135.837594 \nL 232.410771 133.582772 \nL 232.502472 117.047411 \nL 232.685874 74.205793 \nL 232.960977 129.824736 \nL 233.144379 114.792589 \nL 233.32778 137.340809 \nL 233.419481 117.047411 \nL 233.511182 122.308662 \nL 233.602883 97.50562 \nL 233.694584 138.092416 \nL 233.786285 133.582772 \nL 233.969687 114.792589 \nL 234.061388 126.818306 \nL 234.33649 102.766872 \nL 234.428191 62.931683 \nL 234.794995 159.889029 \nL 234.978397 81.721867 \nL 235.070098 92.244369 \nL 235.253499 141.850453 \nL 235.3452 156.130992 \nL 235.620303 108.77973 \nL 235.712004 161.392243 \nL 235.803705 153.87617 \nL 235.895406 156.130992 \nL 235.987107 135.085987 \nL 236.170508 147.111704 \nL 236.35391 86.231511 \nL 236.445611 88.486333 \nL 236.720714 162.143851 \nL 236.904116 140.347238 \nL 237.087517 129.824736 \nL 237.179218 126.066699 \nL 237.36262 161.392243 \nL 237.546022 141.098845 \nL 237.637723 135.085987 \nL 237.821125 90.741155 \nL 237.912826 126.818306 \nL 238.004526 122.308662 \nL 238.096227 123.06027 \nL 238.187928 126.066699 \nL 238.37133 138.092416 \nL 238.463031 139.595631 \nL 238.646433 165.15028 \nL 238.829835 122.308662 \nL 238.921536 157.634207 \nL 239.013236 144.856882 \nL 239.196638 182.437249 \nL 239.38004 133.582772 \nL 239.471741 156.130992 \nL 239.838545 132.079558 \nL 239.930245 138.092416 \nL 240.113647 168.908317 \nL 240.205348 170.411531 \nL 240.38875 117.047411 \nL 240.480451 120.05384 \nL 240.572152 174.169568 \nL 240.663853 169.659924 \nL 240.847254 147.111704 \nL 241.030656 192.208144 \nL 241.214058 168.156709 \nL 241.305759 125.315092 \nL 241.39746 126.066699 \nL 241.489161 144.105275 \nL 241.580862 142.60206 \nL 241.672563 144.105275 \nL 241.764264 162.143851 \nL 241.947665 144.856882 \nL 242.039366 163.647065 \nL 242.314469 152.372955 \nL 242.40617 194.462966 \nL 242.681273 177.175997 \nL 242.772973 171.163139 \nL 242.956375 183.940463 \nL 243.139777 146.360097 \nL 243.231478 155.379385 \nL 243.41488 193.711358 \nL 243.598282 147.863311 \nL 243.689983 174.169568 \nL 243.965085 144.105275 \nL 244.056786 167.405102 \nL 244.148487 162.143851 \nL 244.240188 166.653495 \nL 244.331889 164.398673 \nL 244.42359 203.482254 \nL 244.973795 148.614919 \nL 245.065496 149.366526 \nL 245.248898 142.60206 \nL 245.340599 154.627777 \nL 245.4323 151.621348 \nL 245.524001 153.87617 \nL 245.615701 147.111704 \nL 245.707402 174.921175 \nL 245.799103 147.863311 \nL 245.890804 149.366526 \nL 245.982505 177.927605 \nL 246.165907 158.385814 \nL 246.257608 162.143851 \nL 246.44101 126.066699 \nL 246.532711 140.347238 \nL 246.716112 183.188856 \nL 246.807813 182.437249 \nL 246.899514 154.627777 \nL 246.991215 176.42439 \nL 247.082916 144.105275 \nL 247.174617 146.360097 \nL 247.358019 135.085987 \nL 247.44972 150.118133 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115.544196 \nL 252.218167 140.347238 \nL 252.309867 138.844024 \nL 252.401568 129.824736 \nL 252.493269 136.589202 \nL 252.58497 132.831165 \nL 252.676671 145.608489 \nL 252.951774 113.289374 \nL 253.043475 141.098845 \nL 253.135176 116.295804 \nL 253.226877 141.850453 \nL 253.318577 129.073128 \nL 253.410278 140.347238 \nL 253.685381 41.886678 \nL 253.868783 142.60206 \nL 254.052185 123.811877 \nL 254.143886 132.079558 \nL 254.327287 104.270086 \nL 254.510689 138.844024 \nL 254.694091 117.047411 \nL 254.877493 143.353667 \nL 255.244296 33.618998 \nL 255.427698 134.33438 \nL 255.519399 149.366526 \nL 255.6111 114.792589 \nL 255.794502 140.347238 \nL 255.977904 128.321521 \nL 256.069605 139.595631 \nL 256.161305 110.282945 \nL 256.253006 112.537767 \nL 256.528109 153.124563 \nL 256.61981 144.105275 \nL 256.711511 119.302233 \nL 256.894913 132.079558 \nL 256.986614 129.824736 \nL 257.261716 100.51205 \nL 257.353417 110.282945 \nL 257.62852 81.721867 \nL 257.720221 60.676861 \nL 257.903623 120.805448 \nL 257.995324 132.831165 \nL 258.087024 118.550626 \nL 258.178725 119.302233 \nL 258.270426 130.576343 \nL 258.362127 129.073128 \nL 258.453828 130.576343 \nL 258.63723 119.302233 \nL 258.728931 92.995976 \nL 258.820632 108.028123 \nL 258.912333 107.276516 \nL 259.004033 114.792589 \nL 259.095734 89.23794 \nL 259.370837 113.289374 \nL 259.462538 102.015264 \nL 259.554239 112.537767 \nL 259.829342 74.205793 \nL 259.921043 90.741155 \nL 260.196145 77.212223 \nL 260.287846 46.396322 \nL 260.471248 57.670432 \nL 260.65465 98.257228 \nL 260.746351 89.989547 \nL 260.929752 97.50562 \nL 261.113154 109.531338 \nL 261.204855 97.50562 \nL 261.388257 127.569914 \nL 261.479958 120.05384 \nL 261.846761 38.880249 \nL 262.030163 108.77973 \nL 262.121864 102.015264 \nL 262.213565 105.773301 \nL 262.305266 101.263657 \nL 262.488668 114.040982 \nL 262.580369 145.608489 \nL 262.763771 101.263657 \nL 262.855471 123.811877 \nL 263.130574 90.741155 \nL 263.405677 126.066699 \nL 263.589079 92.995976 \nL 263.77248 113.289374 \nL 264.047583 92.995976 \nL 264.139284 92.995976 \nL 264.230985 114.792589 \nL 264.414387 76.460615 \nL 264.68949 121.557055 \nL 264.78119 97.50562 \nL 265.056293 119.302233 \nL 265.239695 88.486333 \nL 265.331396 89.23794 \nL 265.423097 92.995976 \nL 265.514798 105.773301 \nL 265.606499 139.595631 \nL 265.698199 120.05384 \nL 265.881601 126.066699 \nL 266.156704 96.754013 \nL 266.248405 99.760442 \nL 266.431807 111.78616 \nL 266.615208 97.50562 \nL 266.79861 110.282945 \nL 266.982012 89.23794 \nL 267.073713 98.257228 \nL 267.348816 77.96383 \nL 267.440517 93.747584 \nL 267.532218 90.741155 \nL 267.623918 105.021694 \nL 267.715619 91.492762 \nL 267.80732 112.537767 \nL 267.899021 95.250798 \nL 267.990722 125.315092 \nL 268.082423 104.270086 \nL 268.265825 165.15028 \nL 268.357526 155.379385 \nL 268.540927 96.754013 \nL 268.632628 100.51205 \nL 268.724329 95.250798 \nL 268.907731 152.372955 \nL 268.999432 150.118133 \nL 269.091133 119.302233 \nL 269.182834 135.837594 \nL 269.274535 124.563484 \nL 269.366236 131.32795 \nL 269.457937 117.047411 \nL 269.549637 121.557055 \nL 269.641338 114.792589 \nL 269.733039 95.250798 \nL 269.82474 124.563484 \nL 269.916441 111.78616 \nL 270.008142 82.473474 \nL 270.191544 111.78616 \nL 270.283245 100.51205 \nL 270.374946 105.773301 \nL 270.558347 98.257228 \nL 270.650048 91.492762 \nL 270.83345 120.05384 \nL 270.925151 112.537767 \nL 271.108553 132.079558 \nL 271.200254 124.563484 \nL 271.291955 163.647065 \nL 271.475356 116.295804 \nL 271.567057 113.289374 \nL 271.658758 126.818306 \nL 271.750459 115.544196 \nL 272.117263 153.124563 \nL 272.300665 137.340809 \nL 272.392365 153.87617 \nL 272.484066 149.366526 \nL 272.575767 120.05384 \nL 272.942571 167.405102 \nL 273.401075 120.05384 \nL 273.492776 138.092416 \nL 273.584477 131.32795 \nL 273.676178 149.366526 \nL 273.85958 141.850453 \nL 274.042982 177.175997 \nL 274.134683 165.901887 \nL 274.226384 123.811877 \nL 274.501486 193.711358 \nL 274.593187 186.946892 \nL 274.684888 163.647065 \nL 274.776589 165.15028 \nL 275.051692 155.379385 \nL 275.143393 135.085987 \nL 275.326794 164.398673 \nL 275.510196 139.595631 \nL 275.601897 164.398673 \nL 275.693598 144.105275 \nL 275.785299 144.856882 \nL 275.968701 171.163139 \nL 276.060402 177.927605 \nL 276.152102 177.175997 \nL 276.427205 117.047411 \nL 276.518906 129.073128 \nL 276.610607 163.647065 \nL 276.702308 157.634207 \nL 276.794009 121.557055 \nL 276.88571 161.392243 \nL 276.977411 158.385814 \nL 277.069112 139.595631 \nL 277.160812 174.921175 \nL 277.619317 143.353667 \nL 277.711018 172.666353 \nL 277.986121 150.869741 \nL 278.077821 153.124563 \nL 278.169522 150.869741 \nL 278.352924 141.850453 \nL 278.444625 161.392243 \nL 278.719728 141.098845 \nL 278.811429 153.87617 \nL 278.994831 139.595631 \nL 279.086531 176.42439 \nL 279.269933 162.895458 \nL 279.361634 163.647065 \nL 279.545036 146.360097 \nL 279.636737 185.443678 \nL 279.728438 178.679212 \nL 280.00354 123.811877 \nL 280.095241 121.557055 \nL 280.186942 139.595631 \nL 280.278643 138.844024 \nL 280.370344 141.850453 \nL 280.462045 126.818306 \nL 280.553746 155.379385 \nL 280.645447 150.118133 \nL 280.828849 171.163139 \nL 281.01225 135.085987 \nL 281.103951 164.398673 \nL 281.287353 141.850453 \nL 281.379054 147.111704 \nL 281.562456 100.51205 \nL 281.837559 173.417961 \nL 281.929259 144.105275 \nL 282.02096 148.614919 \nL 282.112661 174.921175 \nL 282.296063 100.51205 \nL 282.571166 163.647065 \nL 282.662867 179.430819 \nL 282.754568 175.672783 \nL 282.846268 163.647065 \nL 282.937969 134.33438 \nL 283.02967 138.844024 \nL 283.213072 141.098845 \nL 283.304773 173.417961 \nL 283.488175 89.989547 \nL 283.671577 153.124563 \nL 283.763278 131.32795 \nL 283.854978 133.582772 \nL 283.946679 148.614919 \nL 284.03838 133.582772 \nL 284.130081 149.366526 \nL 284.221782 121.557055 \nL 284.313483 147.111704 \nL 284.496885 104.270086 \nL 284.771987 169.659924 \nL 284.863688 119.302233 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195.363606 92.010807 \nL 195.455307 92.958992 \nL 195.638709 98.069453 \nL 195.822111 95.110358 \nL 196.005513 99.806152 \nL 196.097213 98.579566 \nL 196.280615 94.619727 \nL 196.464017 102.885338 \nL 196.555718 101.450539 \nL 196.73912 94.430074 \nL 196.922522 102.057943 \nL 197.014222 101.91796 \nL 197.197624 97.060907 \nL 197.381026 100.98025 \nL 197.564428 97.259209 \nL 197.656129 98.375797 \nL 197.839531 103.233714 \nL 198.022932 95.795745 \nL 198.114633 97.171517 \nL 198.298035 105.268181 \nL 198.481437 98.415172 \nL 198.573138 98.594883 \nL 198.75654 104.931797 \nL 198.939941 102.025021 \nL 199.215044 106.788487 \nL 199.398446 103.396126 \nL 199.673549 112.461318 \nL 199.85695 106.242548 \nL 200.132053 116.886664 \nL 200.315455 112.744823 \nL 200.590558 118.676301 \nL 200.682259 117.077039 \nL 200.77396 118.046268 \nL 200.957361 124.517194 \nL 201.140763 118.833279 \nL 201.232464 119.906828 \nL 201.415866 129.338979 \nL 201.507567 127.489738 \nL 201.690969 122.819959 \nL 201.87437 130.163769 \nL 201.966071 129.396777 \nL 202.057772 127.213136 \nL 202.149473 127.882945 \nL 202.332875 131.50016 \nL 202.516277 127.509121 \nL 202.791379 135.686531 \nL 202.974781 128.427329 \nL 203.249884 138.566248 \nL 203.341585 135.808672 \nL 203.433286 133.235893 \nL 203.524987 134.850376 \nL 203.708388 139.454546 \nL 203.800089 137.900351 \nL 203.89179 138.035415 \nL 204.075192 144.636533 \nL 204.166893 143.452734 \nL 204.258594 140.296018 \nL 204.350295 140.917255 \nL 204.533697 151.403369 \nL 204.625397 150.80336 \nL 204.808799 146.311705 \nL 205.083902 156.226257 \nL 205.175603 154.44131 \nL 205.267304 154.960697 \nL 205.450706 160.747624 \nL 205.634107 158.494907 \nL 205.90921 168.383855 \nL 206.092612 162.091281 \nL 206.184313 164.339064 \nL 206.367715 173.22241 \nL 206.551116 167.588544 \nL 206.642817 168.317498 \nL 206.826219 173.493269 \nL 207.009621 170.51154 \nL 207.193023 175.150951 \nL 207.284724 173.926922 \nL 207.468125 168.693294 \nL 207.651527 176.4933 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150.882375 \nL 214.253992 151.569291 \nL 214.437394 156.809246 \nL 214.620796 149.274214 \nL 214.712497 149.318422 \nL 214.804198 151.529877 \nL 214.895899 151.392912 \nL 215.079301 147.4155 \nL 215.262702 152.057143 \nL 215.537805 144.402265 \nL 215.721207 152.854119 \nL 215.812908 151.805539 \nL 215.99631 144.849344 \nL 216.179711 151.588587 \nL 216.271412 151.567262 \nL 216.454814 148.383573 \nL 216.638216 152.270386 \nL 216.821618 147.765127 \nL 216.913319 149.3727 \nL 217.09672 155.296705 \nL 217.280122 147.058708 \nL 217.371823 147.762553 \nL 217.555225 155.174362 \nL 217.830328 147.837935 \nL 218.013729 151.220182 \nL 218.197131 146.642853 \nL 218.380533 149.988036 \nL 218.472234 148.291001 \nL 218.655636 140.898197 \nL 218.839038 147.338167 \nL 218.930738 146.113693 \nL 219.11414 136.291486 \nL 219.205841 137.593247 \nL 219.297542 140.766318 \nL 219.389243 140.375138 \nL 219.572645 133.773976 \nL 219.756047 135.432397 \nL 220.031149 129.000884 \nL 220.214551 133.203335 \nL 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108.699025 \nL 226.725315 102.561142 \nL 226.908717 110.930495 \nL 227.000418 110.365114 \nL 227.18382 102.668824 \nL 227.367222 108.056362 \nL 227.458923 107.793014 \nL 227.642324 103.474297 \nL 227.825726 106.040228 \nL 228.009128 99.614174 \nL 228.100829 100.02126 \nL 228.284231 104.893886 \nL 228.559333 94.130202 \nL 228.742735 100.02676 \nL 229.017838 90.783933 \nL 229.20124 92.864287 \nL 229.384642 87.403984 \nL 229.476342 88.37195 \nL 229.568043 90.529259 \nL 229.659744 89.091547 \nL 229.843146 81.225831 \nL 230.026548 88.184044 \nL 230.118249 88.103253 \nL 230.301651 79.527564 \nL 230.393351 81.142576 \nL 230.576753 86.20046 \nL 230.760155 82.327582 \nL 230.943557 86.899209 \nL 231.035258 86.165377 \nL 231.126959 83.959564 \nL 231.21866 85.075974 \nL 231.402061 93.665546 \nL 231.493762 92.046798 \nL 231.585463 88.381723 \nL 231.677164 88.988512 \nL 231.952267 100.260227 \nL 232.043968 97.62011 \nL 232.135669 97.886429 \nL 232.410771 106.321566 \nL 232.502472 105.862997 \nL 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107.308926 \nL 258.453828 100.718573 \nL 258.545529 101.362849 \nL 258.728931 109.551159 \nL 259.004033 101.716887 \nL 259.187435 109.152771 \nL 259.279136 108.167842 \nL 259.370837 105.469182 \nL 259.462538 105.608912 \nL 259.64594 109.14287 \nL 259.829342 105.21924 \nL 260.104444 111.839441 \nL 260.287846 104.021852 \nL 260.562949 112.633571 \nL 260.746351 105.188292 \nL 260.838052 105.921504 \nL 261.021453 109.162808 \nL 261.204855 105.114288 \nL 261.388257 108.566524 \nL 261.66336 101.080542 \nL 261.846761 108.043406 \nL 261.938462 105.561036 \nL 262.121864 97.729267 \nL 262.305266 104.151874 \nL 262.396967 103.139161 \nL 262.580369 97.980892 \nL 262.763771 101.002559 \nL 262.947172 96.481959 \nL 263.038873 97.838998 \nL 263.222275 102.14655 \nL 263.405677 94.345635 \nL 263.497378 96.057046 \nL 263.68078 103.719883 \nL 263.864181 96.853842 \nL 263.955882 97.419684 \nL 264.139284 103.218453 \nL 264.322686 100.360733 \nL 264.506088 105.262899 \nL 264.597789 104.781465 \nL 264.78119 101.282415 \nL 264.964592 110.196239 \nL 265.056293 109.601776 \nL 265.239695 103.153334 \nL 265.514798 112.508845 \nL 265.698199 108.096296 \nL 265.881601 113.033028 \nL 265.973302 112.419249 \nL 266.065003 110.467807 \nL 266.156704 111.505247 \nL 266.340106 117.176568 \nL 266.523508 110.515239 \nL 266.615208 111.7025 \nL 266.79861 120.424083 \nL 267.073713 113.685482 \nL 267.257115 120.524525 \nL 267.440517 117.564035 \nL 267.532218 118.765835 \nL 267.715619 122.254241 \nL 267.899021 118.696136 \nL 268.174124 127.76469 \nL 268.357526 121.354976 \nL 268.632628 132.467331 \nL 268.81603 128.216153 \nL 269.091133 135.165247 \nL 269.182834 133.846875 \nL 269.274535 134.670188 \nL 269.457937 141.783684 \nL 269.641338 137.220647 \nL 269.733039 138.276159 \nL 269.916441 148.629904 \nL 270.008142 147.527211 \nL 270.191544 143.088615 \nL 270.374946 151.445366 \nL 270.466646 151.330141 \nL 270.558347 149.230699 \nL 270.650048 149.692797 \nL 270.83345 154.031541 \nL 271.016852 150.297011 \nL 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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "train.plot()\n",
    "val.plot()\n",
    "pred_val.plot()\n",
    "print(\"MAPE:\", mape(pred_val, val))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Improvement 3: Detrending\n",
    "Let's try out a different data set that has a global upward trend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "df = pd.read_csv('AirPassengers.csv', delimiter=\",\")\n",
    "ts_2 = TimeSeries.from_dataframe(df, 'Month', ['#Passengers'])\n",
    "train, val = ts_2.split_after(pd.Timestamp('19551201'))\n",
    "train.plot()\n",
    "val.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = FFT()\n",
    "model.fit(train)\n",
    "pred_val = model.predict(len(val))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly, our model fails completely at incorporating the upward trend. Due to the trend, our model also fails to recognize the monthly seasonality."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train.plot()\n",
    "val.plot()\n",
    "pred_val.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This problem can be solved by setting the optional trend argument to either 'poly' or 'exp', which fits a polynomial or exponential funtion to the data and subtracts it before moving on to DFT. When predicting, the trend is added again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = FFT(trend='poly')\n",
    "model.fit(train)\n",
    "pred_val = model.predict(len(val))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have a much better prediction now."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train.plot()\n",
    "val.plot()\n",
    "pred_val.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## New Data: Hourly Nuclear Energy Generation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = pd.read_csv('energy_dataset.csv', delimiter=\",\")\n",
    "df['time'] = pd.to_datetime(df['time'], utc=True)\n",
    "df['time']= df.time.dt.tz_localize(None)\n",
    "\n",
    "ts_3 = TimeSeries.from_dataframe(df, 'time', ['generation nuclear'])\n",
    "ts_3 = fill_missing_values(ts_3, 'auto')\n",
    "train, val = ts_3.split_after(pd.Timestamp('2017-07-01'))\n",
    "train.plot()\n",
    "val.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Instead of simply looking at the performance of the FFT model, we can also look at how a bunch of other forecasting models performs on this new data set in terms of MAPE. Surprisingly, on this dataset, the FFT model outperforms all of the others (at least with their default parameters). Granted, this dataset was specifically chosen because of its highly seasonal nature. However, this shows us that there definitely are use cases for FFT. Furthermore, the FFT model has a much shorter running time than the other models!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Auto-ARIMA MAPE: 13.46753956256134\n",
      "Prophet MAPE: 10.722027903040756\n",
      "Exponential smoothing MAPE: 14.234363362846892\n",
      "Theta(2) MAPE: 13.329984933305795\n",
      "FFT(nr_freqs_to_keep=10, trend=None) MAPE: 10.263184839655274\n"
     ]
    }
   ],
   "source": [
    "models = [\n",
    "    AutoARIMA(),\n",
    "    Prophet(),\n",
    "    ExponentialSmoothing(),\n",
    "    Theta(),\n",
    "    FFT()\n",
    "]\n",
    "\n",
    "for model in models:\n",
    "    model.fit(train)\n",
    "    pred_val = model.predict(len(val))\n",
    "    print(str(model) + \" MAPE: \" + str(mape(pred_val, val)))\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}